Cybernetic group method of data handling (GMDH) statistical learning for hyperspectral remote sensing inverse problems in coastal ocean optics

For complex systems, sufficient a priori knowledge is often lacking about the mathematical or empirical relationship between cause and effect or between inputs and outputs of a given system. Automated machine learning may offer a useful solution in such cases. Coastal marine optical environments represent such a case, as the optical remote sensing inverse problem remains largely unsolved. A self-organizing, cybernetic mathematical modeling approach known as the group method of data handling (GMDH), a type of statistical learning network (SLN), was used to generate explicit spectral inversion models for optically shallow coastal waters. Optically shallow water light fields represent a particularly difficult challenge in oceanographic remote sensing.; Several algorithm-input data treatment combinations were utilized in multiple experiments to automatically generate inverse solutions for various inherent optical property (IOP), bottom optical property (BOP), constituent concentration, and bottom depth estimations. The objective was to identify the optimal remote-sensing reflectance R_rs(λ) inversion algorithm. The GMDH also has the potential of inductive discovery of physical hydro-optical laws. Simulated data were used to develop generalized, quasi-universal relationships. The Hydrolight numerical forward model, based on radiative transfer theory, was used to compute simulated above-water remote-sensing reflectance R_rs(λ) psuedodata, matching the spectral channels and resolution of the experimental Naval Research Laboratory Ocean PHILLS (Portable Hyperspectral Imager for Low-Light Spectroscopy) sensor. The input-output pairs were for GMDH and artificial neural network (ANN) model development, the latter of which was used as a baseline, or control, algorithm. Both types of models were applied to in situ and aircraft data. Also, in situ spectroradiometer-derived R_rs(λ) were used as input to an optimization-based inversion procedure. Target variables included bottom depth z _b, chlorophyll a concentration [chl- a], spectral bottom irradiance reflectance R_b(λ), and spectral total absorption a(λ) and spectral total backscattering b_b(λ) coefficients. When applying the cybernetic and neural models to in situ HyperTSRB-derived R_rs, the difference in the means of the absolute error of the inversion estimates for z_b was significant (α = 0.05). GMDH yielded significantly better z_b than the ANN. The ANN model posted a mean absolute error (MAE) of 0.62214 m, compared with 0.55161 m for GMDH.