Photon path-length distribution function (II)

1994 ◽  
Vol 222 (1-2) ◽  
pp. 47-63 ◽  
Author(s):  
T�nu Viik
Keyword(s):  
Distribution Function ◽  
Path Length ◽  
Length Distribution ◽  
Photon Path

scholarly journals Photon path length distribution in random media from spectral speckle intensity correlations

2011 ◽  
Vol 199 (1) ◽  
pp. 167-180 ◽  
Author(s):  
L. F. Rojas ◽  
M. Bina ◽  
G. Cerchiari ◽  
M. A. Escobedo-Sánchez ◽  
F. Ferri ◽  
...  
Keyword(s):  
Path Length ◽  
Random Media ◽  
Length Distribution ◽  
Photon Path

scholarly journals Photon path length distributions for cloudy skies – oxygen A-Band measurements and model calculations

2003 ◽  
Vol 21 (3) ◽  
pp. 615-626 ◽  
Author(s):  
O. Funk ◽  
K. Pfeilsticker
Keyword(s):  
Radiative Transfer ◽  
Path Length ◽  
Length Distribution ◽  
High Resolution Spectroscopy ◽  
Liquid Water Path ◽  
Model Calculations ◽  
Cloud Structure ◽  
Structure Information ◽  
Radiative Processes ◽  
Photon Path

Abstract. This paper addresses the statistics underlying cloudy sky radiative transfer (RT) by inspection of the distribution of the path lengths of solar photons. Recent studies indicate that this approach is promising, since it might reveal characteristics about the diffusion process underlying atmospheric radiative transfer (Pfeilsticker, 1999). Moreover, it uses an observable that is directly related to the atmospheric absorption and, therefore, of climatic relevance. However, these studies are based largely on the accuracy of the measurement of the photon path length distribution (PPD). This paper presents a refined analysis method based on high resolution spectroscopy of the oxygen A-band. The method is validated by Monte Carlo simulation atmospheric spectra. Additionally, a new method to measure the effective optical thickness of cloud layers, based on fitting the measured differential transmissions with a 1-dimensional (discrete ordinate) RT model, is presented. These methods are applied to measurements conducted during the cloud radar inter-comparison campaign CLARE’98, which supplied detailed cloud structure information, required for the further analysis. For some exemplary cases, measured path length distributions and optical thicknesses are presented and backed by detailed RT model calculations. For all cases, reasonable PPDs can be retrieved and the effects of the vertical cloud structure are found. The inferred cloud optical thicknesses are in agreement with liquid water path measurements. Key words. Meteorology and atmospheric dynamics (radiative processes; instruments and techniques)

Two approaches for assessing photon path length distribution in pulp

2005 ◽  
Author(s):  
Juha Saarela ◽  
Matti Törmänen ◽  
Kyösti Karttunen ◽  
Risto Myllylä
Keyword(s):  
Path Length ◽  
Length Distribution ◽  
Photon Path

scholarly journals Aerosol information content analysis of multi-angle high spectral resolution measurements and its benefit for high accuracy greenhouse gas retrievals

2012 ◽  
Vol 5 (2) ◽  
pp. 2857-2885 ◽  
Author(s):  
C. Frankenberg ◽  
O. Hasekamp ◽  
C. O'Dell ◽  
S. Sanghavi ◽  
A. Butz ◽  
...  
Keyword(s):  
Greenhouse Gas ◽  
Spectral Resolution ◽  
Path Length ◽  
Degrees Of Freedom ◽  
Length Distribution ◽  
High Spectral Resolution ◽  
Atmospheric Variability ◽  
Systematic Biases ◽  
Aerosol Parameters ◽  
Photon Path

Abstract. New generations of space-borne spectrometers for the retrieval of atmospheric abundances of greenhouse gases require unprecedented accuracies as atmospheric variability of long-lived gases is very low. These instruments, such as GOSAT and OCO-2, typically use a high spectral resolution oxygen channel (O2 A-band) in addition to CO2 and CH4 channels to discriminate changes in the photon path-length distribution from actual trace gas amount changes. Inaccurate knowledge of the photon path-length distribution, determined by scatterers in the atmosphere, is the prime source of systematic biases in the retrieval. In this paper, we investigate the combined aerosol and greenhouse gas retrieval using multiple satellite viewing angles simultaneously. We find that this method, hitherto only applied in multi-angle imagery such as from MISR, greatly enhances the ability to retrieve aerosol properties by 2–3 degrees of freedom. We find that the improved capability to retrieve aerosol parameters significantly reduces interference errors introduced into retrieved CO2 and CH4 total column averages. Instead of focussing solely on improvements in spectral and spatial resolution, signal-to-noise ratios or sampling frequency, multiple angles reduce uncertainty in space based greenhouse gas retrievals more effectively and provide a new potential for dedicated aerosols retrievals.

scholarly journals Aerosol information content analysis of multi-angle high spectral resolution measurements and its benefit for high accuracy greenhouse gas retrievals

2012 ◽  
Vol 5 (7) ◽  
pp. 1809-1821 ◽  
Author(s):  
C. Frankenberg ◽  
O. Hasekamp ◽  
C. O'Dell ◽  
S. Sanghavi ◽  
A. Butz ◽  
...  
Keyword(s):  
Greenhouse Gas ◽  
Spectral Resolution ◽  
Path Length ◽  
Degrees Of Freedom ◽  
Length Distribution ◽  
High Spectral Resolution ◽  
Atmospheric Variability ◽  
Systematic Biases ◽  
Aerosol Parameters ◽  
Photon Path

Abstract. New generations of space-borne spectrometers for the retrieval of atmospheric abundances of greenhouse gases require unprecedented accuracies as atmospheric variability of long-lived gases is very low. These instruments, such as GOSAT and OCO-2, typically use a high spectral resolution oxygen channel (O2 A-band) in addition to CO2 and CH4 channels to discriminate changes in the photon path-length distribution from actual trace gas amount changes. Inaccurate knowledge of the photon path-length distribution, determined by scatterers in the atmosphere, is the prime source of systematic biases in the retrieval. In this paper, we investigate the combined aerosol and greenhouse gas retrieval using multiple satellite viewing angles simultaneously. We find that this method, hitherto only applied in multi-angle imagery such as from POLDER or MISR, greatly enhances the ability to retrieve aerosol properties by 2–3 degrees of freedom. We find that the improved capability to retrieve aerosol parameters significantly reduces interference errors introduced into retrieved CO2 and CH4 total column averages. Instead of focussing solely on improvements in spectral and spatial resolution, signal-to-noise ratios or sampling frequency, multiple angles reduce uncertainty in space based greenhouse gas retrievals more effectively and provide a new potential for dedicated aerosols retrievals.

scholarly journals The chord-length distribution of a polyhedron

2020 ◽  
Vol 76 (4) ◽  
pp. 474-488
Author(s):  
Salvino Ciccariello
Keyword(s):  
Distribution Function ◽  
Length Distribution ◽  
Chord Length ◽  
Square Root ◽  
Trigonometric Functions ◽  
Chord Length Distribution ◽  
Analytic Expressions ◽  
Analytic Expression ◽  
Positive Integers ◽  
Inverse Trigonometric Functions

The chord-length distribution function [γ′′(r)] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ′′(r) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R[r, Δ1], Δ1 being the square root of a second-degree r polynomial and R[x, y] a rational function. As r approaches δ, one of the two end points of an r subdomain, the derivative of γ′′(r) can only show singularities of the forms |r − δ|−n and |r − δ|−m+1/2, with n and m appropriate positive integers. Finally, the explicit analytic expressions of the primitives are also reported.

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