Bertrand Chapron

Polarization ratio for microwave backscattering from the ocean surface at low to moderate incidence angles

It has become apparent that as the incidence angle increases from nadir, the ratio of the backscattered power for microwave scattering from the ocean surface at horizontal to that at vertical polarization (HH/VV) becomes larger than that predicted by standard rough-surface scattering models. Although predictions by models that include the effects of long-wave tilt and hydrodynamic modulation yield some improvement, they still underpredict the backscattered power by a factor of two or more. The authors believe that this discrepancy may be partially explained by a more exact treatment of the non-linearity of the long-wave portion of the surface.

Higher–order hydrodynamic modulation: theory and applications for ocean waves

Under the two–scale hydrodynamic model for ocean surface waves, short waves are modulated hydrodynamically by long waves. An exact numerical simulation of the two–scale hydrodynamic process shows that the most commonly used modulation transfer function (MTF), which is a linear approximation, does not capture all of the features caused by the inherent nonlinear nature of the physical processes involved. We rederive the linear MTF and generalize it to include local acceleration and finite depth effects. The phase of the linear MTF is shown to be independent of the direction of long modulating waves. This is an artefact of the linearization of the nonlinear equations. A higher–order theory is also derived based on the truncated Hamiltonian for long modulating waves and dissipation by wave–wave interaction for modulated waves. This new theory includes higher–order derivatives of the source functional and, therefore, short–wave dissipation. Consequently, the phase of the modulation depends on the relative direction of long and short waves. It is shown that while the linear hydrodynamic MTF leads to higher–order statistics equivalent to the bispectrum, the new second–order MTF induces the trispectrum of surface elevation. A succinct derivation for the third–order MTF is given for completeness.

Sea surface slope statistics from a low-altitude aircraft

A new combination of sensors for concurrent aircraft measurement of surface waves and turbulent fluxes has been developed. A simple three laser altimeter arrangement is used to directly measure the 2-D slope of intermediate scale waves and the surface wave profile. A CW scatterometer at Ka-band is used to infer changes in the shorter-scale (less than 1 m) slope variance. This NOAA Long-EZ aircraft then provides high resolution air-sea data with application to such topics as the modulation transfer function, large-scale atmospheric impacts on the sea surface, and characterization of sea surface statistics.

Assessing ocean salinity retrieval using WindSAT data over the Amazone river plume and North Brazil Current retroflection

Measurement of ocean surface salinity (SSS) dynamics from space involve precise determination of the dielectric characteristics of seawater through low-noise passive microwave (MW) radiometer measurement of the oceans brightness temperature (TB), optimally performed at a low frequency near 1.4 GHz (L-band). The future SMOS mission is based on such principles and will aim at retrieving SSS with an accuracy of the order of 0.1 psu (practical salinity units). This represents numerous engineering and scientific challenges, in particular because competing terms carried in the ocean TB measurements, foremost being sea surface temperature (SST) and ocean surface roughness, must be accounted for in a new and more robust manner. Prior to launch, we analyze the sensitivity of the future measurements to these factors by looking at somewhat higher frequency C and X-band data (6.8 and 10.7 versus the L-band 1.4 GHz) that are readily available from several recent MW imagers (AMSR-E, TMI, WindSAT). The shift to C and X-bands lowers TB sensitivity to changes in salinity by a large factor of 10-20. To compensate, we performed our study over the Amazon plume region where there are large (100-200 km) and persistent salinity contrasts that exceed the 0.1 psu science salinity requirement by a factor of 10-40 [1]-[2]. This region is of great importance within the salinity mission context due to the large freshwater flux and northward propagating eddies from retroreflection of the North Brazil Current (NBC). The validity of the emissivity/scattering models developed for SMOS at L-band are analyzed at these higher frequencies and our ability to detect these world largest salinity gradients is assessed.

Consistency in the simulation of microwave remote sensing of the ocean surface in conjunction with a new hydrodynamic theory

Under the two-scale hydrodynamic model for ocean surface waves, short waves are modulated hydrodynamically by long waves. An exact numerical simulation of the two-scale hydrodynamic process shows that the most commonly used modulation transfer function (MTF) is a linear approximation that does not capture all the features caused by the inherent nonlinear nature of the physical processes involved. This lack of information in the linear MTF begs the question: is there a need for a higher-order more consistent theory?.

Inclusion of hydrodynamic modulations to the improved electromagnetic bias theory

The modulation of short ocean waves by longer ones is a likely contributor to the radar altimeters electromagnetic ranging bias (EM-bias). An analytic model to account for this component of the EM bias is developed under a two-scale hydrodynamic assumption. Following the principle of wave action balance, a standard hydrodynamic modulation transfer function is used to establish that the longer modulating waves enter the EM-bias formulation not only through their elevation and slope variables but also through their quadratures. These latter contributions explain the implication of long wave slope and orbital velocity fields in the EM-bias problem. To first order in complexity, analytical expressions are derived using linear Gaussian statistics for both modulating and modulated waves. For sake of completeness, an outline of the possible extension to nonlinear interacting waves is provided.

Short waves in the electromagnetic bias theories

Most previous theories on the altimeter electromagnetic bias (EM-bias) have focused on long waves and their influence through high-order surface statistics. A modification is presented based on the two-scale philosophy where short waves are tilted and modulated by longer ones. Short waves are found to have an essential effect on the EM-bias revealed in the directionality of short wave versus long waves. Known dependence of the EM-bias on radar frequency is also captured by the inclusion of the slope variances of short waves in the final EM-bias formulation. This new theory will be demonstrated using a general numerical simulation. Comparison with empirical models derived from TOPEX/Poseidon data will also be made for various wind speeds and radar frequencies.

Non-linear waves and the electromagnetic bias

The theory of weakly nonlinear (WNL) waves is commonly used in generating higher statistical moments of a random surface wave field. These moments can be used, for example, to estimate the sea state bias (SSB) in radar altimetry under a geometric optical (GO) assumption. The present investigation suggests that several previous SSB studies appear to have misapplied this WNL theory by violating its condition of validity. As a result, a pronounced inconsistency appears even for lower-order moments.