1. FOAM EMISSIVITY MODELS FOR MICROWAVE OBSERVATIONS OF OCEANS FROM SPACE
Magdalena D. Anguelova, Peter W. Gaiser, and
Victor Raizer (presenting)
Remote Sensing Division, Naval Research Laboratory, Washington, DC, USA
Zel Technologies, LLC, Fairfax, VA, USA
July 14, 2009

2. Anguelova, Gaiser, Raizer
Outline
Sea foam and the study problem
Foam emissivity models
Models comparison
Mapping and practical use
Conclusions and future work
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Anguelova, Gaiser, Raizer

3. Motivation: Geophysical retrievals
Radiative transfer equation:
Ocean surface emissivity e:
Sea state:
Small waves;
Large waves;
Foam patches;
Semi-empirical models for e:
Two-scale model for roughness; and
Empirical factor (or correction) for foam;
Wentz & Meissner (2000), Bettenhausen et al. (2006).
Reason: Limited knowledge for sea foam emissivity ef.
To obtain geophysical variables from microwave measurements of the ocean surface brightness temperature, for example wind vector, retrieval algorithms use forward models based on the radiative transfer equation.
Critical quantity in the radiative transfer equation is the emissivity of the ocean surface, e. Sea state, from calm to stormy, determines the ocean surface emissivity. Contributors to the sea state are sea surface roughness--composed of small waves (ripples) and large waves (gravity wind waves and swell)--and foam patches produced by breaking waves. While surface roughness is the main contributor under lower winds, in high-wind conditions (above 7 m/s) the foam becomes increasingly important.
Ocean surface emissivity, e, is usually modeled with semi-empirical models. For example, the physically-based 2-scale model is used to model the roughness, while the contribution from foam is modeled with an empirical factor (e.g., Wentz & Meissner, 2000) or an empirical correction to the roughness emissivity (e.g., Bettenhausen et al., 2006).
The main reason to not be able to model the contribution from foam physically is the limited knowledge for the sea foam emissivity, ef.
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Anguelova, Gaiser, Raizer

4. Anguelova, Gaiser, Raizer
Sea foam definition
Oceanographic definition:
Whitecaps on the surface;
Bubble plumes below.
Remote-sensing definition
Skin depth at microwave frequencies:
a few mm to  1 cm;
Radiometers detect only the surface foam layers:
Thin foam stripes and
Patches of foam (whitecaps).
For oceanographers both bubble rafts floating on the surface and bubble plumes below the surface are considered sea foam and are important for various air-sea interaction processes.
But from remote-sensing perspective, the skin depth at microwave frequencies (from a few mm to 1 cm) determines that radiometers detect only the surface part of the sea foam.
So, in microwave terminology we are interested in the surface foam layers, which we see the ocean as thin foam stripes and patches of foam or whitecaps.
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Anguelova, Gaiser, Raizer

5. Anguelova, Gaiser, Raizer
Problem statement
Sea foam structure:
Vertical stratification of foam properties;
Closely packed bubbles;
Requirements to model ef:
Vertical profile;
Absorption AND scattering;
Previous models:
Empirical—only radiometric and enviromental variables, NO foam characteristics:
Stogryn (1972);
Wilheit (1978);
Physical—with foam characteristics BUT:
Droppleman (1970):
NO profile, NO scattering;
Rosenkranz and Staelin (1972)
Profile, but NO scattering;
Tsang and colleagues, 2001 – 2003:
Scattering, but NO profile.
z = 0
z = h
Air
fa  100%
ε0 = 1
Water
fa  0% ε
fa(z)
εf(z)
Photo: Camps et al. (2005)
Let’s take a close look at a layer of sea foam as shown in this photograph. There are two major observations:
First, the foam structure changes gradually from the air-foam interface at z = 0 down into the foam-layer depth, say z = h. In the upper part of the foam layer we see large, thin-walled bubbles. This foam has high void fraction fa (close to 100%) or this is dry foam. The bubbles become smaller and with thicker walls in the foam depth. This structure contains more water making wet foam. These changes in the foam structure and foam void fraction with depth cause vertical stratification of the foam dielectric properties as well, from air-like in the upper part of the foam layer to seawater-like in foam depth.
The second observation in this photographs is the close packing of the bubbles.
These two observations lead to the two major requirements for a foam emissivity model. Namely, a foam emissivity model needs to consider:
First, a vertical profile of all foam properties and
Second, not only the absorption in the foam but also the scattering among the bubbles forming the foam.
Different foam emissivity models address these two requirements differently.
Empirical models (Stogryn, 1972; Wilheit, 1978) do not consider the foam characteristics at all. They give foam emissivity in terms of radiometric (e.g., frequency and incidence angle) and environmental (wind and SST) variables. The physically-based models do consider foam characteristics, but they address the requirements we establish here differently, as the list of models shows.
In this study ... (here click and go to the next slide)
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Anguelova, Gaiser, Raizer

6. Foam emissivity models
Compare two models:
Macroscopic foam-spray model (Raizer, 2007) R07; ;
Radiative transfer model for foam (Anguelova et al., 2006) A06;
Similar: both account for vertical profile of
Void fraction fa(z)
Effective foam permittivity (complex dielectric constant) εf(z);
Different: in 3 elements:
Parameterization of fa(z);
Mixing rule for εf(z);
Model computing the foam emissivity ef;
Objective: Evaluate the differences between the two models due to the
different elements;
Compare models in terms of:
Absolute bias:
Percent difference:
...we compare two foam emissivity models, namely
the macroscopic foam-spray model of Raizer (2007) and
the Radiative transfer model for foam of Anguelova et al. (2006).
These models are similar in that they both address the vertical profile of the foam properties, i.e., the models incorporate
void fraction profile fa(z) and
foam permittivity profile epsilon(z).
These models differ in 3 elements:
The functional form of the void fraction profile;
The mixing rule for foam permittivity, which include or ignore scattering among bubbles, and
The model for computing the foam emissivity.
The objective, therefore, of our study was to evaluate the differences between the two models due to these different elements.
We compare the two emissivity models in terms of:
Absolute bias and
Percent difference
defined as shown with these formulae.
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Anguelova, Gaiser, Raizer

7. Anguelova, Gaiser, Raizer
Models main elements
R07 (Raizer, 2007)
Sea foam as a multilayer dielectric structure (spray switched off);
Void fraction: hyperbolic tangent
Mixing rule for εf(z): combination of
Odelevskiy formula (no scattering);
Scattering with modified Lorentz-Lorenz (L-L) formula;
Model for foam emissivity ef
n dielectric layers, εn;
Complex Fresnel reflection coefficients, rn.
A06 (Anguelova et al. (2006)
Sea foam as one layer;
Void fraction: exponential
Mixing rule for εf(z):
Refractive law;
Scattering ignored:
Review shows scattering is weak in foam;
Anguelova (2008);
Model for foam emissivity ef :
Incoherent approach of solving RTE (Ulaby et al., 1986);
Suitable for weak scattering;
More specifically, the models we compared have the following elements:
Model R07
represents the sea foam as a multilayer dielectric structure including layers of mono-dispersed bubbles, poly-dispersed bubbles, polyhedral bubbles, and sea spray. For this study the sea spray is switched off.
The void fraction profile is modeled with hyperbolic tangent.
The effective foam permittivity is computed as a combination of Odelevskiy formula and the modified Lorentz-Lorenz formula, which accounts for the scattering among bubble by incorporating in the calculations bubble size distribution.
The model computing the foam emissivity ef is an iterative numerical method, which calculates complex Fresnel reflection coefficients of a large number of elementary layers (n), each characterized with a specific complex dielectric constant and thickness.
Model A06
Considers the foam as one layer
The void fraction profile follows exponential profile with coefficients determined from the boundary conditions.
The effective complex dielectric constant is calculated with the Refractive (quadratic) model, which does not account for scattering. The rational to ignore the scattering in foam is based on the conclusion Anguelova made in a 2008 paper that scattering in foam is weak.
The model computing the foam emissivity ef is the so-called incoherent approach of solving the radiative transfer equation, which is considered suitable for weakly scattering medium.
eBf =
Upwelling
Scattering
Downwelling
Transmitted through foam
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Anguelova, Gaiser, Raizer

8. Mixing rules and scattering account
Odelevskiy
Scattering included via:
L-L mono-dispersed bubbles
L-L poly-dispersed bubbles
Re{f}
Im{f}
Odelevskiy
Refractive
No scattering
Re{f}
Im{f}
These graphs show the real and imaginary parts of foam permittivity predicted by mixing rules with and without scattering.
The upper two panels show the relative amplitudes of the foam permittivity that is used in model R07. We see that the Odelevskiy formula (green lines in the graphs) is too low at high void fractions and that when the scattering from poly-dispersed bubbles (red lines) is combined with it, the permittivity values of dry foam increase substantially. Meanwhile, combining the Odelevskiy formula with the scattering of mono-dispersed bubbles (blue lines) would only slightly change the permittivity values for wet foam.
The lower two panels show how Odelevskiy formula (green lines again) compares with the Refractive mixing rule (black lines) used in model A06. The permittivity values for wet foam are very similar from both formulae, but for dry foam, the Refractive law predicts higher values. This means that even though model A06 ignores scattering, the use of the Refractive law has the potential to compensate for it. The results we show latter confirm this expectation.
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Anguelova, Gaiser, Raizer

9. Anguelova, Gaiser, Raizer
Models comparisons
Case #
Model
fa(z)
f formula
L-L scatt
ef model
How ef is affected by
Results 1
R07
lin
Odel No
Fresnel
Choice of ef model
Main models
differences
< 5% up to 100%
A06
RTM 2
Yes
Including scattering
Models biases
change from
Case #1 by
< 20% 3
Use Refractive law
Lowest models
biases!
Refr 4
tanh
fa(z) functional form
increase more
than in Case #2
exp
We compared models R07 and A06 in 4 cases each time with one model element changed or added. In this way we evaluate how different model elements affect the models predictions of foam emissivity.
The elements we consider, highlighted here with yellow, are : the functional form of the void fraction; the effective foam permittivity with and without scattering; and the model for computing ef.
In Case #1 both models use the same, linear profile for the void fraction and calculate foam permittivity with Odelevskiy formula, that is, scattering is not included in this case. The only difference that remains between the two models (shown here in red) is how ef is computed, with Fresnel reflections or with the incoherent approach of solving RTE. This case, therefore, quantify the difference between R07 and A06 due to the model choice for computing ef.
Mouse click or right arrow on the keyboard for animation:
In case #2 all elements in model A06 are the same, while in R07 we change only the computation of foam permittivity to include scattering with L-L formula. In this way we quantify the effect of including scattering on foam emissivity ef.
In case #3 all elements are as in case #2 only the computation of foam permittivity in model A06 is changed from Odel formula to Refractive law. This case, therefore, can verify Anguelova’s conclusion that the Refractive law is more suitable than other mixing rules for computing foam permittivity when scattering is ignored.
Finally, case #4 quantifies differences between the two models due to use of different functional forms for the void fraction profile, hyperbolic tangent versus exponential.
The overall results of these comparisons are shown here.
Case #1 shows that the main differences between models R07 and A06 are due to the choice of the model computing ef. These differences could be above 20% up to 100% for thin foam layers (1 cm) and lower frequencies (below 5 GHz), H polarization. In most cases, however—frequencies above 5 GHz, V pol and thick foam (above 1 cm)—the models differ by no more than 20%.
Case #2 shows that when scattering is included, the differences between the models change (increase or decrease) by no more than 20%. That is, the choice of ef model is more consequential than including or ignoring scattering.
Case #3 shows the lowest differences between models. We interpret this as confirmation that using the refractive law to obtain foam permittivity compensates to some degree the ignoring of scattering.
Case #4 shows that the models are quite sensitivity to the functional form of the void fraction. All the gain from case #3 was lost and the differences increased even above those of Case #2, especially for thin foam at H pol.
In the next slide we show the results for cases 3 and 4.
Graph
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Anguelova, Gaiser, Raizer

10. Anguelova, Gaiser, Raizer
Numerical results
ef modeled with different inputs
ef biases due to different inputs
Case #3
(Case #2)
(Case #3)
(Case #4)
Here are some numerical results for the modeled emissivity. Shown are the “worst case” scenarios, that is, results for thin foam (1 cm), H pol. For thicker foam and V pol the differences are much smaller.
On the left we have the emissivity values from both models. In the upper panel scattering is included in R07 via L-L formula and scattering is compensated in A06 to some extend with the refractive law. We see how close the predictions for ef are.
In the lower panel the functional forms of the void fraction profiles are changed from linear to tangent-hyperbolic for R07 and exponential for A06. We see the that there is larger disparity between the models for both H and V pols. As compared to the upper panel. This means that the ef predictions are sensitive to the choice of the functional form of the void fraction.
The differences between the ef values in these graphs are quantified in the graph to the right. We see that the emissivity biases between the two models are smallest for case #3 and largest for case #4. The biases for H pol are larger than those for V pol.
Case #4
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Anguelova, Gaiser, Raizer

11. Brightness temperature due to foam
‘Modeled’ TBf
‘Measured’ TBf
TBf mapping ef W Ts
TB(WS)
TB(2s)
Matched up
Lat, Lon
TB , U10 , Ts , AC
Monahan and O'Muircheartaigh (1986)
2-scale roughness
model, no foam
Bettenhausen et al. (2006)
U10
U10,Ts AC
A foam emissivity model predicts the emissivity of an area fully covered with foam. To put these modeled values of foam emissivity into practical use, we show here (with the red blocks) how they can be used to obtain the brightness temperature TB due to foam for ocean conditions. In addition we compare these modeled TBf with first estimates of TB due to foam from satellite-based data (shown with the green blocks).
Let’s start with the modeling and mapping of TB due to foam (red blocks).
With a foam emissivity model (here R07 and A06) we calculate ef at 10 oC, salinity of 34 psu, frequencies from 1 to 100 GHz, H and V pols., incidence angle of 53 deg, and at foam thicknesses from 1 cm to 10 cm.
These ef values are combined with the physical seawater temperature Ts and the foam fraction W to obtain TB due to foam in the ocean.
The foam fraction W can be obtained using wind speed U10 with one of the various parameterizations available in the literature. The results shown in the next slides use the parameterization of Monahan and O'Muircheartaigh (1986) for neutral atmosphere. But we used other formulae for W and concluded that the main uncertainty in obtaining modeled TBf comes from the choice of W(U10) parameterization. We note that here we red shading of the block for W.
Ts and U10 can be obtained from satellites (e.g., QuikSCAT) or from weather prediction models (e.g., GDAS at NCEP, Global Data Assimilation System at National Centers for Environmental Prediction). The modeled TB due to foam, TBfmod, is mapped over the ocean using the (lat,lon) locations of U10 and Ts.
The green blocks at right visualize our procedure of obtaining the measured brightness temperature due to foam.
For this we use WindSat measurements of TB at the top of the atmosphere (TOA) matched in time and space with U10 and Ts from QuikSCAT and GDAS.
We also use the WindSat forward model to obtain TB due to rough surface with the 2-scale model. The 2-scale model is tuned for roughness only and does not include the effect of foam. It is ran with the U10 and Ts match-ups.
Match-ups with data from SSMI (Special Sensor Microwave Imager) are used to make atmospheric correction of the TB from WindSat and from the 2-scale model and obtain TB at the ocean surface.
Taking the difference between these two surface estimates, TB(WS) and TB(2s), we obtain the measured TB due to foam.
These measured TBf values are mapped on the globe and compared with the corresponding maps of modeled TBf.
The differencing TB(WS)-TB(2s) minimizes the uncertainty due to atmospheric correction and match-ups. Error analysis shows that error due to inaccuracies in U10 and Ts are small, at most 2%. The main uncertainty in estimating measured TBf comes from modeling errors in the 2-scale model, which are difficult to quantify. This is marked here with green shading of the ‘2-scale’ block.
In the following slides I will show examples of measured and modeled TBf, as well as difference maps, for North Atlantic, North Pacific and the Southern Ocean.
Ts=10 oC, S=34 psu
=53, F=1-100 GHz, H&V, h=1 cm
R07 Raizer (2007)
A06 Anguelova et al. (2006)
WindSat TOA TB
Gaiser et al. (2004)
Shaded blocks show main source of uncertainty.
U10
QuikSCAT JPL Data ctr Ts
GDAS/NCEP
Atm. Corr. (AC)
SSM/I, Wentz, RSS
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Anguelova, Gaiser, Raizer

12. Compare modeled & measured
WindSat
North Atlantic
Jan 2006
37 GHz, H pol
Absolute values
The first example is for North Atlantic, January 2006, 37 GHz. As before in the graphs, we show the “worst case” scenario, that is, H pol and 1-cm foam thickness. For V pol and thicker foam, the differences are imperceptible.
All maps are in the WindSat swath resolution with pixels spaced along and across the satellite track at about 12.5 km and a value for each pixel obtained from a footprint of 50 km x 70 km. This is the low WindSat resolution. Higher WindSat resolutions are available, with each pixel value obtained from a footprint of 25 km x 35 km, but these are not use in the present study.
The map at right shows the measured TBf from WindSat data, ranging from 0 to 18 K.
The maps at left are modeled TBf values obtained with models R07 and A06. We see that the two models predict very similar spatial distribution of TBf, only model R07 shows slightly lower values than A06.
This is better visualized with the difference map...mouse click or right arrow of the keyboard to go to the next slide...
R07
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Anguelova, Gaiser, Raizer

13. Compare modeled & measured
WindSat
North Atlantic
Jan 2006
37 GHz, H pol
Biases: Model - WindSat
...here we show the differences between each model and the WindSat estimates, model minus WindSat. The fact that both difference maps are mostly bluish means that both models usually underestimate the measured TBf and show overestimation (pink) only in a few places.
The area-averaged absolute bias between model and measurements are: 2 K for model A06 and 2.7 K for R07
The mean PD (percent difference) is 48% for A06 and 57% for R07.
These comparing metrics change when another formula is used for the foam fraction W(U10) and model R07 compares better with the measured TBF than model A06. So, I re-iterate, the main uncertainty comes not from the foam emissivity models, but from the parameterization of the foam fraction.
R07
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Anguelova, Gaiser, Raizer

14. Compare modeled & measured
WindSat
North Atlantic
Jan 2006
10 GHz, H pol
Absolute values
This is the same region and time, North Atlantic, January 2006, but the maps are for 10 GHz, H pol. Instead of 37 GHz.
The spatial differences that we note here, some overestimation by A06 and some lower values by R07 as compared to the WindSat values, are quantified in the difference maps... Click or arrow to go to the next slide...
R07
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Anguelova, Gaiser, Raizer

15. Compare modeled & measured
WindSat
North Atlantic
Jan 2006
10 GHz, H pol
Biases: Model - WindSat
The lighter blue color of these maps shows that the underestimation here is lower than the underestimation at 37 GHz. The biases and PDs are much smaller. Once again, the performance of the two models is different if another foam fraction parameterization is used.
R07
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Anguelova, Gaiser, Raizer

16. Compare modeled & measured
WindSat
A06
Southern Ocean
Aug 2006
10 GHz, H pol
Absolute values
These are maps of the modeled and measured TBf for 10 GHz in the Southern Ocean, Aug click or arrow to go to the next slide...
R07
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Anguelova, Gaiser, Raizer

17. Compare modeled & measured
WindSat
A06
Southern Ocean
Aug 2006
10 GHz, H pol
Biases: Model - WindSat
... and the corresponding difference maps.
R07
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Anguelova, Gaiser, Raizer

18. Anguelova, Gaiser, Raizer
Conclusions
Two basic foam microwave models are considered and compared in details;
Bubble’s properties are the main microstructure factor;
Effective permittivity and emissivity values are computed for a wide range of frequencies from 1 to 100 GHz;
Effects of scattering and dielectric stratifications (profiles) are evaluated numerically;
Scattering and profiles contributions affect models prediction most in frequency range from 1 to 40 GHz;
Both models are suitable for ocean studies from space;
So-called “Foam coverage signatures” are generated from WindSat and model data for the first time.
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Anguelova, Gaiser, Raizer

19. Anguelova, Gaiser, Raizer
Future work
Develop more detailed models with different (empirical) combined profiles;
Provide comparisons with other models and experimental data;
Expand formula L-L from dipole to multi-pole approach (taking into account Mie scattering for bubbles);
Consider foam coverage with horizontal nonuniformities and apply averaging by the thickness and antenna beam;
Model maps with variable thickness of foam coverage;
Use in algorithm for retrieval of foam coverage from WindSat data;
IGARSS’09 February 17, 2019February 17, 2019
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20. Additional, extended, or alternative slides

21. Anguelova, Gaiser, Raizer
Sea foam
Motivation:
Geophysical retrievals (e.g., wind vector):
Weather prediction models;
Climate studies;
Ocean surface emissivity in the radiative transfer equation:
Limited knowledge for sea foam emissivity ef.
Definition:
Skin depth at microwave frequencies:
a few mm to  1 cm;
Consider only the surface foam layers:
Thin foam stripes and
Patches of foam (whitecaps).
Retrievals of geophysical variables from microwave measurements of the ocean surface brightness temperature, for example wind vector, are important for
Weather prediction models and
Climate studies.
The retrieval algorithms use the radiative transfer equation and critical quantity in it is the emissivity of the ocean surface, e. Sea state, from calm to stormy, determines the ocean surface emissivity. Contributors to the sea state are sea surface roughness--composed of small waves (ripples) and large waves (gravity wind waves and swell)--and foam patches produced by breaking waves. While surface roughness is the main contributor under lower winds, in high-wind conditions (above 7 m/s) the foam becomes increasingly important.
Ocean surface emissivity, e, is usually modeled with semi-empirical models. For example, the physically-based 2-scale model is used to model the roughness, while the contribution from foam is modeled with an empirical factor (e.g., Wentz & Meissner, 2000) or an empirical correction to the roughness emissivity (e.g., Bettenhausen et al., 2006).
The main reason to not be able to model the contribution from foam physically is the limited knowledge for the sea foam emissivity, ef.
For oceanographers both bubble rafts floating on the surface and bubble plumes below the surface are considered sea foam and are important for various air-sea interaction processes.
But from remote-sensing perspective, the skin depth at microwave frequencies (from a few mm to 1 cm) determines that radiometers detect only the surface part of the sea foam.
So, in microwave terminology we are interested in the surface foam layers, which we see the ocean as thin foam stripes and patches of foam.
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Anguelova, Gaiser, Raizer

22. Macroscopic foam model (R07)
Sea foam as a multilayer dielectric structure;
Spray switched off;
Void fraction: hyperbolic tangent
Mixing rule for εf(z): combination of
Odelevskiy formula (no scattering);
Modified Lorentz-Lorenz (L-L) formula: accounts for scattering among bubbles;
Model computing the foam emissivity ef
represent εf(z) with n dielectric layers, εn;
Consecutive calculations of the complex Fresnel reflection coefficients, rn.
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Anguelova, Gaiser, Raizer

23. Radiative transfer model (A06)
Sea foam as one layer;
Void fraction: exponential
Mixing rule for εf(z):
Refractive law;
Scattering ignored;
Model computing the foam emissivity ef :
Incoherent approach of solving RTE;
Suitable for weak scattering;
Calculates different contributions.
eBf =
Upwelling
Scattering
Downwelling
Transmitted seawater
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Anguelova, Gaiser, Raizer

24. Specifics of the emissivity models
Model name
fa(z)
f (z)
Scatt
ef model
Scheme
R07
tanh
Odel formula
L-L formula
Fresnel reflection coeff.
A06
exp
Refraction law
No scatt
RTM
Raizer (2007)
eBf =
Anguelova et al (2004)
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Anguelova, Gaiser, Raizer

25. Mixing rules without scattering
Odelevskiy in R07;
To be combined with L-L formula to account for scattering.
Refractive law in A06 model;
Scattering ignored with expected error up to 15%
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26. Contributions to f from scattering
Accounted for in model R07;
With L-L formula applied for:
Mono-dispersed foam (L-L mono)
predominantly small bubbles
characteristics of wet foam
in the middle and lower part of a foam layer;
Poly-dispersed foam (L-L poly)
predominantly of large bubbles
characteristics of dry foam
in upper part of a foam layer.
Graphs show:
L-L mono and L-L poly similar;
Add to no scattering in dry foam;
Lower f values in wet foam;
Results:
L-L mono and L-L poly contributions are quite similar at the chosen bubble parameters.
In dry foam (high void fractions) both L-L mono and L-L poly add to the no-scattering (Odelevsky) values
at void fractions above 76%, where the importance of scattering is expected to be the highest;
For wet foam, accounting for the scattering lowers the values of the foam permittivity.
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Anguelova, Gaiser, Raizer

27. Anguelova, Gaiser, Raizer
Models comparisons
Case #
Model
fa(z)
f formula
L-L scatt
ef model
How ef is affected by
Results 1
R07
lin
Odel No
Fresnel
Choice of ef model
Highest models
differences
< 5% up to 100%
A06
RTM 2
Yes
Including scattering
Models biases
increase from
Case #1 by
< 20% 3
Use Refractive law
Lowest models
biases!
Refr 4
tanh
fa(z) functional form
increase more
than in Case #2
exp
Graph
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Anguelova, Gaiser, Raizer

28. Anguelova, Gaiser, Raizer
Numerical results
PD = 5%
F = 5 GHz
Lowest models differences
Sensitivity to void profile form
(Case #2)
(Case #2)
(Case #3)
(Case #3)
(Case #4)
Here are graphs showing how the percent differences between the models compare for cases 2 to 4. Shown are the “worst case” scenarios, that is, results for thin foam (1 cm), H pol. For thicker foam and V pol the differences are much smaller.
The left panel shows how the use of refractive law (case 3) decreases the differences between the models.
The right panel shows how the use of different void fraction profiles worsen the comparison between the models.
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Anguelova, Gaiser, Raizer

29. Case #3: Lowest models biases
For this case we run the two models with all elements as before except that this time we include scattering with L-L formula in R07 model.
Model A06 again does not account for scattering and still uses Odelevkiy formula for the foam permittivity as in R07.
The differences between the two models when scattering is included are smaller than the differences due to the model choice shown on the previous slide. We illustrate this by plotting this time the absolute biases of the foam emissivity as a function of freq for H and V pol. and the worst case for foam thickness, 1 cm.
Here the black lines are the differences in foam emissivity at H and V pol. from the previous run (model choice)
The blue lines are the differences due to both model choice and scattering.
The red lines show the difference of these two biases. That is, the red lines represent the biases between the two models due solely to scattering inclusion in the R07 model.
The observations from this graphs are (read on the slide).
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

30. Case #4: fa(z) functional form
Much lower differences for h > 1 cm
For this case we run the two models with all elements as before except that this time we include scattering with L-L formula in R07 model.
Model A06 again does not account for scattering and still uses Odelevkiy formula for the foam permittivity as in R07.
The differences between the two models when scattering is included are smaller than the differences due to the model choice shown on the previous slide. We illustrate this by plotting this time the absolute biases of the foam emissivity as a function of freq for H and V pol. and the worst case for foam thickness, 1 cm.
Here the black lines are the differences in foam emissivity at H and V pol. from the previous run (model choice)
The blue lines are the differences due to both model choice and scattering.
The red lines show the difference of these two biases. That is, the red lines represent the biases between the two models due solely to scattering inclusion in the R07 model.
The observations from this graphs are (read on the slide).
Graph: ef in PD (%)
Observations:
For V pol all h:
F > 5 GHz, PDs << 5%;
F < 5 GHz, PDs > 20%;
For H pol., thin foam:
The gain of using Re law is lost;
F > 5 GHz, PD < 26%;
F < 5 GHz, PD > 26%;
Models are sensitive to void fraction model;
Need to research the most realistic profile for fa(z).
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

31. Effect of model choice on ef
ef model
L-L scatt
f (z)
fa(z)
R07 No
Odel
Lin
A06
fa = Air
Water fa = 0 h
R07 Odel
A06 Odel
Graph: ef in PD (%)
Observations:
ef >0  A06 predicts always higher ef ;
Smaller PDs for V pol;
Largest PD at H pol. for thin layers (1 cm);
ef  15% for F > 4 GHz
Both models, R07 and A06, are ran with the same elements, namely:
Linear void fraction profile;
Odelevskiy formula for effective foam permittivity
No scattering is included.
The differences between the two models are due solely on the model chosen to compute the foam emissivity,
Fresnel reflection coef. in layered structure for R07 and
Incoherent approach to RTE solution for A06.
The graph shows percent differences in foam emissivity as a function of freq for H and V pol. at 3 foam-layer thicknesses.
The observations from this graphs are (read on the slide).
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

32. Effect of including scattering
ef model
L-L scatt
f (z)
fa(z)
R07
Yes
Odel
Lin
A06 No
fa = Air
Water fa = 0 h
R07 Odel
A06 Odel
L-L
fa = const
Graph: ef in Absolute biases
Observations:
For all cases—H and V pol and all foam thicknesses—at all frequencies calculated that:
PDs are at most 20% and
usually less than 10%;
We conclude that inclusion/omission of the scattering in foam contributes less differences between models than the model choice for ef .
Both models, R07 and A06, are ran with the same elements, namely:
Linear void fraction profile;
Odelevskiy formula for effective foam permittivity
No scattering is included.
The differences between the two models are due solely on the model chosen to compute the foam emissivity,
Fresnel reflection coef. in layered structure for R07 and
Incoherent approach to RTE solution for A06.
The graph shows percent differences in foam emissivity as a function of freq for H and V pol. at 3 foam-layer thicknesses.
The observations from this graphs are (read on the slide).
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

33. Effect of using Refractive law
ef model
L-L scatt
f (z)
fa(z)
R07
Yes
Odel
Lin
A06 No
Refr
fa = Air
Water fa = 0 h
R07 Odel
A06 Refr
L-L
fa = const
Graph: ef in PD (%)
Observations:
For H and V pol all h:
F > 5 GHz, PDs < 5%;
F < 5 GHz, PDs > 20% only for thin foam.
The use of Refractive law reduces the diffs between models;
Refractive law compensates for scatt with the expected error of at most 20%, and usually << 5%, for most frequencies.
For this case we run the two models with all elements as before except that this time we include scattering with L-L formula in R07 model.
Model A06 again does not account for scattering and still uses Odelevkiy formula for the foam permittivity as in R07.
The differences between the two models when scattering is included are smaller than the differences due to the model choice shown on the previous slide. We illustrate this by plotting this time the absolute biases of the foam emissivity as a function of freq for H and V pol. and the worst case for foam thickness, 1 cm.
Here the black lines are the differences in foam emissivity at H and V pol. from the previous run (model choice)
The blue lines are the differences due to both model choice and scattering.
The red lines show the difference of these two biases. That is, the red lines represent the biases between the two models due solely to scattering inclusion in the R07 model.
The observations from this graphs are (read on the slide).
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

34. Effect of fa(z) representation
ef model
L-L scatt
f (z)
fa(z)
R07
Yes
Odel
Tanh
A06 No
Refr
Exp
fa = Air
Water fa = 0 h
R07 Odel
A06 Refr
L-L
fa = const
Graph: ef in PD (%)
Observations:
For V pol all h:
F > 5 GHz, PDs << 5%;
F < 5 GHz, PDs > 20%;
For H pol., thin foam:
The gain of using Re law is lost;
F > 5 GHz, PD < 26%;
F < 5 GHz, PD > 26%;
Models are sensitive to void fraction model;
Need to research the most realistic profile for fa(z).
For this case we run the two models with all elements as before except that this time we include scattering with L-L formula in R07 model.
Model A06 again does not account for scattering and still uses Odelevkiy formula for the foam permittivity as in R07.
The differences between the two models when scattering is included are smaller than the differences due to the model choice shown on the previous slide. We illustrate this by plotting this time the absolute biases of the foam emissivity as a function of freq for H and V pol. and the worst case for foam thickness, 1 cm.
Here the black lines are the differences in foam emissivity at H and V pol. from the previous run (model choice)
The blue lines are the differences due to both model choice and scattering.
The red lines show the difference of these two biases. That is, the red lines represent the biases between the two models due solely to scattering inclusion in the R07 model.
The observations from this graphs are (read on the slide).
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

35. Brightness temperature due to foam
‘Modeled’ TBf
ef from R07 and A06;
Foam fraction:
Monahan and O'Muircheartaigh (1986)
Ts = 0 (neutral atmosphere)
U10 from QuikSCAT;
Ts from GDAS/NCEP;
‘Measured’ TBf
TB (WS) from WindSat data;
TB (2s) from 2-scale model:
Tuned for roughness only;
Foam NOT included;
Data for 2-scale model:
U10 from QuikSCAT;
Ts from GDAS/NCEP;
Atmospheric correction with SSM/I data;
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

36. Compare modeled & measured
WindSat
North Pacific
Mar 2006
37 GHz, H pol
R07
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

37. Compare modeled & measured
WindSat
North Pacific
Mar 2006
37 GHz, H pol
R07
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

38. Region 1: North Atlantic, Jan 2006
SST (oC)
Min = 3.6
Max = 16.3
Mean = 11.6
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

39. Region 2: North Pacific, March 2006
SST (oC)
Min = 8.3
Max = 24.5
Mean = 18.2
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

40. Region 3: Southern Ocean, August 2006
SST (oC)
Min = -1.
Max = 20.9
Mean = 10.7
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer

41. Anguelova, Gaiser, Raizer
Conclusions more
We compared two foam emissivity models, which address differently the vertical stratification of and scattering in foam:
Raizer (2007) and
Anguelova et al. (2006);
Overall, predictions of foam emissivity with both models differ from less than 5% to up to 100% depending on the frequency, polarization, and foam thickness;
The choice of ef model is the most important choice;
The inclusion or omission of scattering in a foam emissivity model is not critical;
Refractive law for foam permittivity f(z) can compensate for ignoring scattering;
Foam emissivity models are sensitive to the functional form of the void fraction profile fa(z);
Foam emissivity models are not a limiting factor in estimating the brightness temperature due to foam, TBf, over the ocean; the foam fraction W(U10) is.
In conclusion:
We compared two foam emissivity models, Raizer (2007) and Anguelova et al. (2006), which address differently the vertical stratification of and scattering in foam;
Overall, predictions of foam emissivity with both models differ from less than 5% to up to 100% depending on the frequency, polarization, and foam thickness;
The choice of ef model is the most important choice;
The inclusion or omission of scattering in a foam emissivity model is not critical;
Refractive law can compensate for ignoring scattering;
Foam emissivity models are sensitive to the functional form of the void fraction profile;
Foam emissivity models are not limiting factor in estimating TBf over the ocean, the foam fraction is.
IGARSS’09 February 17, 2019February 17, 2019
Anguelova, Gaiser, Raizer