Improving the optimization solution for a semi-analytical shallow water inversion model in the presence of spectrally correlated noise
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In coastal regions, shallow water semi-analytical inversion algorithms may be used to derive geophysical parameters such as inherent optical properties (IOPs), water column depth, and bottom albedo coefficients by inverting sensor-derived sub-surface remote sensing reflectance, rrs. The uncertainties of these derived geophysical parameters due to instrumental and environmental noise can be estimated numerically via the addition of spectral noise to the sensor-derived rrs before inversion. Repeating this process multiple times allows the calculation of the standard error and average for each derived parameter. Apart from spectral non-uniqueness, the optimization algorithm employed in the inversion must converge onto a single minimum to obtain a true representation of the uncertainty for a given set of noise-perturbed rrs. Failure to do so inflates the uncertainty and affects the average retrieved value (accuracy). We show that the standard approach of seeding the optimization with an arbitrary, fixed initial guess, can lead to the convergence to multiple minima, each having substantially different centroids in multi-parameter solution space. We present the Update-Repeat Levenberg-Marquardt (UR-LM) and Latin Hypercube Sampling (LHS) routines that dynamically search the solution space for an optimal initial guess, that when applied to the optimization allows convergence to the best local minimum. We apply the UR-LM and LHS methods on HICO-derived and simulated rrs and demonstrate the improved computational efficiency, precision, and accuracy afforded from these methods compared with the standard approach. Conceptually, these methods are applicable to remote sensing based, shallow water or oceanic semi-analytical inversion algorithms requiring nonlinear least squares optimization.
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