1. Microwave Emissivity of a Vertically Inhomogeneous Sea-Foam Layer: Application to the WindSat Retrieval Algorithm
Magdalena D. Anguelova, Karen St. Germain,
Craig Smith, Peter Gaiser, Richard Bevilacqua,
Nai-Yu Wang, Michael Bettenhausen
We work on physically-based forward model for WindSat retrieval algorithm and the effect of sea foam is part of it. In this presentation I will talk on one aspect of our work on sea foam.
Remote Sensing Physics Branch
Naval Research Laboratory
21 September, 2004

2. WindSat forward model Radiative transfer equation:
Semi-empirical surface model:
e = er + Δe
2-scale model for er;
WindSat data for Δe.
WindSat forward model is based on RTE. My colleague Nai-Yu Wang described earlier today the terms in these equations.
Foam enters surface emissivity e and reflectivity r.
As my colleague Mike Bettenhausen presented today, we currently have a semi-empirical surface model, in which we use two-scale model for rough-sea emissivity and foam effects to some extend, and WindSat data to add an empirical correction to account further for foam and for some modeling errors.

3. Complete physical model
Surface emissivity:
Difficulties in modeling e:
Two-scale model limitations;
Limited knowledge for ef ;
Separate er and ef ;
High uncertainty for f ;
Simultaneously, we work on complete physical model, in which surface emissivity is presented with its full expression: emissivity of rough sea in foam-free places, and emissivity of foam in foam-covered areas.
This full model for surface emissivity has not been used until now due to several difficulties:
* 2-scale model still has some uncertainties;
* The knowledge on foam emissivity is incomplete;
* It is almost impossible to clearly separate rough-sea and foam emissivities without new measurements;
* And there is high uncertainty in the existing parameterizations of foam fraction.
We work on all these aspects, but today I will present some concepts and results on the foam emissivity.

4. Sea foam Whitecaps on the surface Bubble plumes below the surface
Both, bubble rafts floating on the surface, and bubble plumes below the surface are considered sea foam. But while bubble plumes are important for gas exchange and turbulent mixing studies, for us the surface whitecaps are of interest, not only for remote sensing, but also for climate studies, for example, production of sea-salt aerosols. These surface foam patches are our study subject today.

5. Foam void fraction
This is a close look of the foam layer floating on the surface. Main characteristics of this foam is void fraction defined as...
The void fraction changes in depth -- the amount of air is maximum at the surface and it gradually decreases in depth.
The reason is that foam structure changes with depth.
At the surface, there are large bubbles (up to 2 cm diameter) with very thin walls (just a few micrometers) so that the surface part of the foam layer contains little water.
In depth, the bubble sizes decrease (down to about 200 micrometers) and the bubble walls thicken (up to several hundred micrometers), so this part of the layer hold more water.

6. Foam dielectric constantε'
ε"
6.8 GHz
37.0 GHz
18.7 GHz
Void fraction together with the dielectric constant of seawater are used to calculate dielectric constant of foam.
Both, real and imaginary parts of foam dielectric constant are presented here as a function of void fraction at 3 frequencies.
High void fraction in the upper part of the foam layer makes the dielectric properties of foam close to those of air -- the real part is close to 1, the imaginary part, which is a measure for the losses of a media, is negligibly small.
Low void fraction in the lower part of the foam layer makes the foam dielectric constant close to that of seawater -- large dielectric constant with significant attenuation.
As a result of this change in the foam dielectric properties with depth, foam matches the impedances of two very distinct media -- air and seawater.

7. Matching impedances air seawater
Here are the impedances of air and seawater for all WindSat frequencies, as you see, quite different due to very different dielectric constants.
Since the reflection is proportional to the impedance difference, we observe strong reflection at the air-water interface and only a small part of incoming radiation would be transmitted and available for attenuation and consequent emission. The same is true for the radiation emitted from seawater and propagating upward: at the interface most will be reflected back, and only small part will leave the water and be registered. As a result, ocean has low emissivity.

8. Matching impedances air seawater air foam (98%) foam (10%) seawater
Things change when foam with changing dielectric properties is at the interface.
Upper part of the foam layer with high void fraction, decreases the impedance difference at the air-foam interface.
Lower part of the foam layer with low void fraction, decreases the impedance difference at the foam-water interface.
As a result, only small part of the incoming radiation will be reflected at the surface and most will be available for attenuation and then emission.
Same is true for the outgoing emitted radiation.
As a result, foam-covered ocean has high emission.

9. Mechanisms of attenuation
Tdown
Tsc
Absorption:
85%-90%;
Small in bubble walls;
Max at water boundary;
Scattering:
10%-15%;
λ-dependent.
0.72
1.1
1.31
2.1
3.2
λf cm
fa= 98%
0.20
0.26
0.28
0.41
0.60
fa= 10%
1.3
23.8
0.8
37.0
1.6
18.7
2.8
10.7
4.4
6.8
λ0 cm
F GHz
The main attenuation mechanism in foam are, of course, absorption and scattering.
Experiments have shown that their contributions to the signal registered from foam-covered areas are quite different.
85 to 90% of the radiation is absorbed in foam, and only 10 to 15% is scattered.
In addition, it has been proven experimentally that most of the absorption takes place close to the foam-water border. It is small in the upper part because large bubbles with thin walls cannot provide enough water for absorption. Quick estimates show that we may need 1 m thick foam with high void fraction to absorb whatever 1 mm water can absorb.
At the same time, since scattering is is wavelength dependent, it occurs in the entire layer. As void fraction decreases in depth, so does the wavelength of the radiation propagating through the foam. And since the bubble sizes decrease in depth too, at any level within the layer there will be some scattering.
Max bubble dia 2 cm
Min bubble dia 0.02 cm

10. Foam-covered area TB Reflection/scattering terms; Emission terms. TBf
z = 0
The signal from a foam-covered area has several contributions.
Besides the reflection and scattering terms, there will be up welled emission from the foam, down welled emission, and emission from the water below the layer.
In addition, there will be multiple reflections that will also direct some radiation toward an observing radiometer.
z = -d
TBf = + + + +

11. Model requirements Vertically inhomogeneous layer;
Absorption and scattering;
Various contributions to foam emission.
Droppleman, 1970
Rosenkranz and Staelin, 1972
So, we can summarize, that a model for foam emission has to address the following issues: *
Both empirical and analytical models have been offered for foam emissivity and they meet these requirements in different degree and with different approaches.
Some analytical models involve the macro characteristics of the foam, for example void fraction and thickness,
Others use foam microphysical characteristics, such as bubble size distribution and thickness of bubble walls.
Raizer and colleagues
1982, 1992
Chen et al., 2003

12. Foam emission
Brightness temperature due to foam as a function of wind speed is plotted here for 4 models -- Droppleman, Stogryn, Wentz, and St. Germain.
While Wentz and St. Germain model foam implicitly with empirical corrections and tuning, Droppleman and Stogryn represent explicit analytical and empirical models for foam emissivity, they do not contain dependence on wind speed. The wind speed dependence is introduced in Droppleman and Stogryn models with Monahan’s parameterization of foam fraction and is the reason for the specific trend.
I can discuss specifics of the calculations later if this is of interest.
We will compare our results with these models.

13. Our choice Macro characteristics (layer);
Vertically inhomogeneous (depth profile);
Flat specular boundaries;
Incoherent approach -- weak scattering;
Ignore scattering term;
Our specific choices for modeling foam are:
z = 0
Air, ε0=1
Foam, ε (z)
z = -d
Water, ε

14. Void fraction profile

15. Foam dielectric constant

16. Foam attenuation coefficient

17. Foam refraction

18. Foam emission components
+ diffuse scattering term dz

19. Foam emission componentsdz

20. Foam emission componentsdz

21. Foam emission componentsdz

22. Foam contributions TBf0 = + + + + d/0  0.02 d/0= 0.25 d =0/50
4 mm
TBf0 = + + + +

23. TBf over distribution of thickness
Reising et al., 2002

24. Foam emission
Having this new set of parameters, we ran the WindSat forward model and used the results to see what changes in emissivity and TB we can expect due to foam. The figure shows TB as a function of wind speed.
The black lines are …
The upper red line is result of WindSat algorithm tuned for foam via er. We remove from this result the model output for rough sea emissivity and obtain …
… the lower red line, which shows that TB due to foam should be of this order. This line is our reference in the work of modeling foam emissivity

25. Foam emission

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