Microwave Emissivity of a Vertically Inhomogeneous SeaFoam Layer

Wind. Sat forward model q Radiative transfer equation: q Semi-empirical surface model: e =

Complete physical model q Surface emissivity: q Difficulties in modeling e: v v Two-scale

Sea foam q Whitecaps on the surface q Bubble plumes below the surface

$Foam void fraction$

Foam dielectric constant ε' ε" 6. 8 GHz 18. 7 GHz 37. 0 GHz

Matching impedances air seawater air foam (98%) seawater foam (10%)

Mechanisms of attenuation Tdown q Absorption: v 85%-90%; v Small in bubble walls; v

Foam-covered area TB q Reflection/scattering terms; q Emission terms. z=0 z = -d TBf

Model requirements q Vertically inhomogeneous layer; q Absorption and scattering; q Various contributions to

$Void fraction profile$

$Foam refraction$

Foam emission components + diffuse scattering term dz

Foam contributions d/ 0 0. 02 d = 0/50 320 m TBf 0= +

TBf over distribution of thickness Reising et al. , 2002

$Necessary experiments q Void fraction profile; q Values for boundary conditions; q Bubble size$

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Microwave Emissivity of a Vertically Inhomogeneous Sea-Foam Layer: Application to the Wind. Sat Retrieval Algorithm Magdalena D. Anguelova, Karen St. Germain, Craig Smith, Peter Gaiser, Richard Bevilacqua, Nai-Yu Wang, Michael Bettenhausen Remote Sensing Physics Branch Naval Research Laboratory 21 September, 2004

Wind. Sat forward model q Radiative transfer equation: q Semi-empirical surface model: e = er + Δe v 2 -scale model for er; v Wind. Sat data for Δe.

Complete physical model q Surface emissivity: q Difficulties in modeling e: v v Two-scale model limitations; Limited knowledge for ef ; Separate er and ef ; High uncertainty for f ;

Sea foam q Whitecaps on the surface q Bubble plumes below the surface

$Foam void fraction$

Foam void fraction

Foam dielectric constant ε' ε" 6. 8 GHz 18. 7 GHz 37. 0 GHz

Matching impedances air seawater

Matching impedances air seawater air foam (98%) seawater foam (10%)

Mechanisms of attenuation Tdown q Absorption: v 85%-90%; v Small in bubble walls; v Max at water boundary; Tsc q Scattering: v 10%-15%; v λ-dependent. Max bubble dia 2 cm Min bubble dia 0. 02 cm F GHz λ 0 cm λf cm fa= 98% λf cm fa= 10% 6. 8 4. 4 3. 2 0. 60 10. 7 2. 8 2. 1 0. 41 18. 7 1. 6 1. 31 0. 28 23. 8 1. 3 1. 1 0. 26 37. 0 0. 8 0. 72 0. 20

Foam-covered area TB q Reflection/scattering terms; q Emission terms. z=0 z = -d TBf = + +

Model requirements q Vertically inhomogeneous layer; q Absorption and scattering; q Various contributions to foam emission. Droppleman, 1970 Rosenkranz and Staelin, 1972 Raizer and colleagues 1982, 1992 Chen et al. , 2003

Foam emission

Our choice q Macro characteristics (layer); q Vertically inhomogeneous (depth profile); q Flat specular boundaries; q Incoherent approach -- weak scattering; q Ignore scattering term; z=0 Air, ε 0=1 Foam, ε (z) z = -d Water, ε

$Void fraction profile$

Void fraction profile

Foam dielectric constant

Foam attenuation coefficient

$Foam refraction$

Foam refraction

Foam emission components + diffuse scattering term dz

Foam emission components dz

Foam contributions d/ 0 0. 02 d = 0/50 320 m TBf 0= + d/ 0= 0. 25 d = 0/4 4 mm + + +

TBf over distribution of thickness Reising et al. , 2002

Foam emission

$Necessary experiments q Void fraction profile; q Values for boundary conditions; q Bubble size$

Necessary experiments q Void fraction profile; q Values for boundary conditions; q Bubble size distribution; q Thickness distribution; q Azimuthal dependence.