The electromagnetic (EM) bias is the largest source of error in the TOPEX/Poseidon and Jason-1 satellite sea surface height (SSH) estimates. Due to incomplete understanding of the physical processes which cause the bias, current operational models are based on empirical relationships between the bias wind speed and significant wave height. These models reduce RMS estimation errors of the EM bias to approximately 4 cm. To improve EM bias estimation the correlation between the bias and RMS long wave slope is studies using data from tower-based experiments in the Gulf of Mexico and Bass Straight, Australia. Models based on significant wave height and RMS slope are more accurate than models based on wave height and wind speed by at least 50% in RMS error between predicted and ground truth bias values. Nonparametric models have been proposed as a method to reduce the variability of EM bias estimates. Using tower data, nonparametric models developed from wind speed and significant wave height measurements are shown to provide some improvement over parametric models. It is also shown that the historical discrepancy between satellite and tower EM bias measurements is reduced by nonparametric modeling. A validity study of rough surface scattering models is conducted for surfaces with Gaussian and power law power spectra. Models in the study include physical optics (PO), geometrical optics, small perturbation method, and small slope approximation. Due to the prevalence of the PO approximation, particular emphasis is placed on the development of a validity criterion for the PO model. An empirical study of the PO approximation shows that the validity of the model is more accurately described by the RMS wave slope than the classic surface curvature criterion for surfaces with a Gaussian power spectrum. For surfaces with a power law PSD, the accuracy of the PO approximation is related to the significant slope (RMS surface height/wavelength of the dominant spectral peak). The validity of other models in the study are also shown to be well approximated by bounds on surface slope. An EM bias model is derived using the physical optics scattering model, hydrodynamic modulation, and non-Gaussian long wave surface statistics. Using a modulation transfer function, the hydrodynamic modulation of small wave heights is shown to be linearly related to the long wave RMS slope. The resulting EM bias model expresses the relative bias as a function of the long wave surface parameters RMS wave slope, surface skewness, and tilt modulation. Coefficients of the long wave parameters are determined by the short ocean waves, and provide insight into the physical mechanisms that cause the bias. From measured values of the ocean surface profile, estimated values of the bias are computed from the bias model. A comparison of these estimated values with in situ EM bias measurements shows a strong correlation between the estimated and measured values. Nadir and off-nadir measurements of the EM bias collected during the BYU Off-Nadir Experiment (Y-ONE) are presented. The in situ measurements are compared with bias estimates computed from an off-nadir generalization of the nadir EM bias model. From theoretical and experimental bias measurements a model of the angular dependence of the bias is developed as a function of the normalized bias at nadir.

In May of 2000 Jason-1, a joint project between NASA and the French space agency CNES, will be launched. Its mission is to continue the highly successful gathering of data which TOPEX/Poseidon has collected since August of 1992. The main goal of Jason-1 is to achieve higher accuracy in measuring the mean sea level (MSL). In order to do so, the electromagnetic (EM) bias must be estimated more accurately because it is the largest contributing error. This thesis presents two different studies which add to the knowledge and improve estimation of the EM bias, and thus assists Jason-1 in achieving its primary goal. Oceanographic data collected from two different experiments are analyzed; on in the Gulf of Mexico (GME) and the other in Bass Strait, Australia (BSE). The first study is a spatial analysis of the backscattered power versus the phase of the wave. Its purpose is to determine why the normalized EM bias stops increasing and levels out at high wind speeds (about 11 m/s) and then decreases at higher wind speeds. Two possible causes are investigated. First, it could be due to a shift in the backscatter power modulation to the forward or rear face of the wave crests. Second, it may be due to the backscatter power becoming more homogeneous throughout the wave profile. This study is novel because it uses the knowledge of the spatial distribution of both the backscatter and wave displacement for the study of the EM bias. Both contribute to the EM bias decrease, but the latter cause seems to be the dominant effect. This study is performed on GME data. The second study uses two different nonparametric regression (NPR) techniques to estimate the EM bias. A recent study of satellite data from the TOPEX/Poseidon altimeter supports that the bias is modeled better using NPR regression. A traditional parametric fit is compared to two NPR techniques with GME data. The parametric fit is a variation of NASA's equation used to estimate EM bias for their Geophysical Data Records (GDRs). The two NPR techniques used are the Nadaraya-Watson Regression (NWR) and Local Linear Regression (LLR) estimators. Two smoothing kernel functions are used with each NPR technique, namely the Gaussian and the Epanechnikov kernels. NPR methods essentially consist of statistically smoothing the measured EM bias estimates are compared in the wind and significant wave height plane. Another recent study has shown that wave slope is strongly correlated to EM bias. With this knowledge, EM bias is estimated over several two-dimensional planes which include wave slope in attempt to reduce the residual bias. This portion of the study is performed on GME and BSE data. It is shown that a combination of slope, significant wave height, and wind speed used in conjunction with these NPR methods produces the best EM bias estimate for tower data.

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