Parameterization of the Aerosol Upscatter Fraction as Function of the Backscatter Fraction and Their Relationships to the Asymmetry Parameter for Radiative Transfer Calculations
Abstract
:1. Introduction
2. Average Aerosol Upscatter Fraction
3. Henyey-Greenstein (HG) Phase Function, Asymmetry Parameter, and Its Range in the Atmosphere
3.1. Henyey-Greenstein (HG) Phase Function and Asymmetry Parameter g
3.2. Range of the Asymmetry Parameter
3.2.1. Principal Considerations
3.2.2. Mie Calculations of the Asymmetry Parameter g
3.2.3. Measurements of the Asymmetry Parameter g in the Ambient Atmosphere
3.3. Backscatter Fraction for Henyey-Greenstein (HG) Phase Function: Solutions and Approximations
3.4. Upscatter Fraction for Henyey-Greenstein (HG) Phase Function: Solutions and Approximations
3.5. Relationship and Approximations between Average Upscatter Fraction and Backscatter Fraction for Henyey-Greenstein (HG) Phase Function
3.5.1. Approximation by Hegg, et al. [24]
3.5.2. Approximation by Sheridan and Ogren [32]
4. Conclusions
- b(g)
- Equation (8), analytical, exact;
- g(b)
- Equation (10), third order polynomial approximation with RSME = 0.0051;
- Equation (14), third order polynomial approximation with RSME = 0.0029;
- Equation (15), fifth order polynomial approximation with RSME = 0.0031.
Acknowledgments
Conflicts of Interest
Symbols
Name | Symbol | Unit |
aerosol asymmetry parameter | g | |
aerosol backscatter fraction | b | |
aerosol optical thickness | τ | |
aerosol radiative forcing | ΔFaer | W/m2 |
atmospheric transmittance above aerosol layer | Tatm | |
average aerosol upscatter fraction | β | |
fractional cloud cover | Acld | degree |
particle radius | r | m |
particle size parameter | x | |
refractive index, complex | m | |
refractive index, real | n | |
refractive index, imaginary | k | |
scattering angle | θ | degree |
scattering efficiency | Qsca | |
scattering phase function | p | |
single scattering albedo | ω | |
solar constant | s0 | W/m2 |
solar zenith angle | θ0 | degree |
surface reflectance | Rsurf |
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Range of g | Method | Location | Reference |
---|---|---|---|
0.36–0.71 | Novel Algorithm | Global NOAA Network | Fiebig and Ogren [18] |
0.5–0.8 | Mie Retrieval | Oklahoma, USA | Andrews, et al. [5] |
0.3–0.6 | Nephelometer Retrieval | Tropical India | Ramachandran and Rajesh [20] |
0.53–0.65 | Nephelometer Retrieval | Southern India | Gopal, et al. [21] |
0.72–0.73 | Mie Retrieval | Canari Islands, Spain | Formenti, et al. [22] |
0.44–0.72 | Nephelometer Retrieval | Marine West Coast, USA | Hegg, et al. [23] |
0.37–0.75 | Nephelometer Retrieval | Prudhoe Bay, AK, USA | Hegg, et al. [24] |
0.40–0.66 | Nephelometer Retrieval | Negev Desert, Israel | Ichoku, et al. [25] |
0.26–0.77 | Nephelometer Retrieval | Northern, Mid-Latitudes | Andrews, et al. ([26]; Figure 3f) |
0.34–0.73 | Nephelometer Retrieval | Melpitz, East Germany | Ma, et al. [27] |
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Moosmüller, H.; Ogren, J.A. Parameterization of the Aerosol Upscatter Fraction as Function of the Backscatter Fraction and Their Relationships to the Asymmetry Parameter for Radiative Transfer Calculations. Atmosphere 2017, 8, 133. https://doi.org/10.3390/atmos8080133
Moosmüller H, Ogren JA. Parameterization of the Aerosol Upscatter Fraction as Function of the Backscatter Fraction and Their Relationships to the Asymmetry Parameter for Radiative Transfer Calculations. Atmosphere. 2017; 8(8):133. https://doi.org/10.3390/atmos8080133
Chicago/Turabian StyleMoosmüller, Hans, and John A. Ogren. 2017. "Parameterization of the Aerosol Upscatter Fraction as Function of the Backscatter Fraction and Their Relationships to the Asymmetry Parameter for Radiative Transfer Calculations" Atmosphere 8, no. 8: 133. https://doi.org/10.3390/atmos8080133