Manifold Learning and Graphical Statistical Characterization of Ocean Thermal-Momentum Structure Using Array Observations

Ocean drilling is a hazardous enterprise fraught with the possibility of oil spill accidents which can cause millions of dollars of damage to the environment.The 2010 Gulf of Mexico oil spill was responsible for detrimental changes to surrounding bio-chemical ecosystems over both short and long spatio-temporal scales.These sorts of oceanic disasters necessitate the need to understand the thermal-momentum dynamics which drive the spread of oil as well as how physical variables become modulated by fluid contaminants.Machine learning-based analysis is believed to be a valuable aid in this endeavor and was applied to temperature and velocity data acquired from an array of bottom mounted acoustic Doppler current profilers situated near Mobile Bay off the coast of Mississippi.Preliminary analysis of temperature data from 6 profilers covering the upper 6.5 m of the water column showed a 1-degree Celsius temperature increase over a 10-day spring time span in April 2016.This low thermal change was characterized by a slow stable temperature increase over 7 days followed by an increase in temperature variance over the last 3 days.The thermal change consistently appeared in two-dimensional manifolds generated by principal component analysis, Laplacian eigenmap analysis, t-distributed stochastic neighbor embedding, and non-negative matrix factorization as a separable, latent space two-cluster structure.Bayesian belief network analysis of the temperature array data spanning a 25 km spatial scale over the full time span displayed strong evidence of turbulent mixing with a temperature covariance structure suggesting heat transport from east to west along the Mississippi coast as well heat transport in both the offshore and onshore directions.Bayesian belief network analysis of the accompanying velocity magnitude showed a current velocity covariance structure suggesting significant momentum flux in the offshore direction into the deep waters of the Gulf of Mexico.Weak momentum flux in the east-to-west direction was suggested by the Bayesian belief network calculated over the first 7 days.Link strength analysis of temperature and velocity magnitude Bayesian belief network edges supported the presence of the twocomponent manifold latent space thermal structure.The slow increase in the large spatial scale temperature field over the first 7 days was partially characterized by a momentum nave Bayesian sub-network.Nave Bayesian classification parameterized the velocity magnitude dynamics of a 3-node linear network situated perpendicular to the Mississippi coast with an average predictive error of 38%, providing additional evidence of the anisotropic offshore momentum flux over the spatial scale of the array.The turbulent mixing regime dynamics occupying the last 3 days was parameterized using a single mooring location via Markovian covariant statistical modeling of wave variance with temperature.The hidden Markov model transition matrix for wave variance demonstrated a trend where increasing wave variance has a tendency of transitioning into low wave variance.This was possibly indicative of the time-to-event statistical structure of the wave variance over the 10-day time span with the data showing the repetitive tendency of wave variance growth followed by a transition to a low variance.The emission matrix, where wave variance was modeled as the state variable and temperature as the observation variable, showed a weak pattern of low wave variance associated with low temperature and high wave variance associated with high temperature.Medium level wave variance was associated with a spread of temperature intervals which is possibly associated with turbulent mixing-based transport of heat.The ability of machine learning analysis to provide a data driven summary of the coastal thermal and momentum dynamics suggests that it could support online machine learning-based data analytics for coastal environmental monitoring.