Current Projects: Modeling Microwave Backscatter from the Ocean

INTRODUCTION

A multiscale model of microwave backscatter from the sea surface has been constructed and run for various radar and environmental conditions.  This model builds on the Small Slope Approximation of Voronovich (Sov. Phys. JETP, Engl. Transl., 62,1985) and the Integral Expansion Method of Fung, Li, and Chen (IEEE TGRSS, 30, 1992).  A simple expression consistent with both theories was produced and shown to reduce to Bragg scattering for small surface displacements.  Multiscale aspects of the model come in because the surface was broken into three different scales and the longer scales were assumed to modulate the shorter scales.  This modulation not only changes amplitudes and frequencies of shorter waves but changes the local incidence angle that must be used in the simple expression to calculate results.  Predictions of the model for incidence angles out to 50 degrees were compared with our data collected on an airship and with a variety of other data collected by others.  The results showed very good agreement between the model and data for incidence angles from nadir out 50 degrees.  See Plant, JGR, 29(22) 2002 for more details

At higher incidence angles, bound wave effects must be included in the modeling work.  We have found that even with these effects in the model, HH backscattering cross sections are too low at high incidence angles.  For moderate incidence angles and for VV polarized backscatter at incidence angles up to about 80 degrees, we have found Bragg scattering / composite surface theory to provide a very good explanation of all aspects of the data.  Bragg / composite explains the probability distributions of backscattering amplitude (the square root of cross section) as well as the probability of HH cross sections being larger than VV.  This later aspect of the data is a result of fading in the Bragg backscatter.  We have found that Non-Bragg surface scattering is not necessary to explain it.  We have postulated that Non-Bragg scattering that is not from the surface may enter the problem at HH polarization and high incidence angles in the form of scattering from spray droplets above the ocean surface. 

THE MULTISCALE MODEL

In Plant, JGR, 29(22) 2002 we showed that both the Small Slope Approximation and the Integral Expansion Method yield the same expression for the backscattering cross section of the sea,  σ_qp where q and p indicate transmit and receive polarizations.  This expression yields the Bragg scattering result, σ_os, when the surface may be considered to be slightly rough.  The relevant equations are the following:

In these equations, k_o is microwave number, θ is incidence angle, σ² is mean square surface slope, ρ is the surface correlation function, F_s is the small-scale surface wave variance spectral density, ε is the dielectric constant, and primes indicate local quantities.

The multiscale model consists of applying the first equation above to three different scales of surface displacement, keeping effects of smaller scales in the mean square slope, and letting the incidence angle be the local one that includes effects of tilting by larger scales.  Figure 1 shows a diagram of the model.

Figure 1.  Diagram of the multiscale model of the ocean surface.  Scattering types from the different scales are indicated as Bragg for the small-scales and IEM (or SSA) for the intermediate scales where the full integral for σ_qp must be solved.  Large scales scatter little at any low to moderate incidence angle.

One output of this model is an indication of the fraction of the backscatter that can be described as Bragg scattering.  Figure 2 shows this fraction as a function of wind speed at three different low to moderate incidence angles.

Figure 2.  Fraction of backscatter that can be described as Bragg scattering as a function of wind speed at three different incidence angles according to the multiscale model..

The model has been exercised at a variety of incidence angles, azimuth angles, wind speeds and microwave frequencies.  Figures 3 and 4 give examples of the agreement of the model with data.

Figure 3.  Comparison of the predictions of the multiscale model at nadir with data from the Topex/Poseidon altimeter.  Solid and dashed lines are predictions of the model using two different wave spectral forms when backscatter from intermediate scale waves is calculated by numerically evaluating the integral.  Dotted and dash-dotted lines are the predictions with a stationary phase approximation to the integral.

Figure 4.  Comparison of the azimuthally averaged cross section predicted by the multiscale model using three different wave spectral forms with data collected on an airship (Plant et.al., 1998).

MICROWAVE SEA RETURN AT MODERATE TO HIGH INCIDENCE ANGLES

The multiscale model presently is not valid beyond about 50 degree incidence angles because bound waves have not been included in it.  As a first step to adding these effects, we have modeled the fading response of microwave sea return at moderate to high incidence angles including the effects of bound waves (Plant, 2003).  Many properties of this response such as the probability of finding HH cross sections greater than VV, the probability distribution of the scattering amplitude, and the probability distribution of the polarization ratio can be adequately explained by Bragg scattering at moderate incidence angles.   Figures 5 and 6 show this for an incidence angle of 45 degrees.  The data were collected during Phase II of the SAXON-FPN experiment in 1991.

Figure 5.  Distributions of cross sections and polarization ratios at a 45 degree incidence angle looking upwind.  Left column shows data from Phase II of SAXON-FPN.  Right column shows the results of Bragg scattering simulations.

Figure 6.  Probability distributions of scattering amplitudes at a 45 degrees incidence angle looking upwind.  The amplitude a_o is the square root of the average cross section.  Left column shows data from Phase II of SAXON-FPN.  Right column shows results of Bragg scattering simulations.

We have found that this agreement cannot be obtained from the procedures embodied in the multiscale model as in stands, that is, including only freely propagating short waves.  However, simply adding Bragg scattering from bound wave effects has proven to be insufficient to explain all the effects shown above because HH backscatter is not increased sufficiently by this procedure.  In order to get the same quality of agreement between data and model at higher incidence angles, we have had to add both bound wave effects and a additional Gaussian field.  Figures 7 and 8 show the results of this procedure at a 75 degree incidence angle.

Figure 7.  Distributions of cross sections and polarization ratios at a 75 degree incidence angle.  Left column are data from Phase II of SAXON-FPN.  Right column are Bragg scattering simulations including both free and bound waves and a Gaussian field of magnitude (10^-3.3)^1/2.

Figure 8.  Probability distributions of scattering amplitudes at a 75 degrees incidence angle looking upwind.  The amplitude a_o is the square root of the average cross section.  Left column shows data from Phase II of SAXON-FPN.  Right column shows results of simulations including Bragg scattering from both free and bound waves and a Gaussian field of magnitude (10^-3.3)^1/2.

We have suggested that the small amount of extra backscatter, on the order of σ_o = -33 dB, that becomes apparent in HH backscatter when the Bragg scattering cross section drops below this level might be due to scattering from spray droplets above the sea surface.  Our calculations indicate that a droplet density on the order of  2 drops per cubic meter would be enough to account for this level of backscatter.  More details can be found in Plant, 2003.