Improving Electromagnetic Bias Estimates

IMPROVING ELECTROMAGNETIC BIAS ESTIMATES Floyd W. Millet Electrical and Computer Engineering Doctor of Philosophy 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.