Date of Award

Spring 2021

Degree Type

Open Access Dissertation

Degree Name

Computational Science Joint PhD with San Diego State University, PhD


Institute of Mathematical Sciences

Advisor/Supervisor/Committee Chair

Jose E. Castillo

Dissertation or Thesis Committee Member

Chris Paolini

Dissertation or Thesis Committee Member

Peter Blomgren

Dissertation or Thesis Committee Member

Ali Nadim

Terms of Use & License Information

Creative Commons Attribution-Noncommercial 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License

Rights Information

© Copyright Manuel Alonzo Valera, 2021 All rights reserved.


Coastal Ocean Dynamics, Machine Learning, Mimetic Operators, Navier Stokes, Time series forecast


Nonlinear internal waves are a ubiquitous and fundamental aspect of the coastal ecosystem understanding. However, they rely on extreme geographical conditions and precise dimensional equilibrium to be captured accurately. The General Curvilinear Coastal Ocean Model (GCCOM) was validated, serial and parallel versions for a set of experiments showcasing stratified and non-hydrostatic flow phenomena. Still, the 3D curvilinear capability has proven to be elusive. We apply cutting-edge numerical methods to improve upon the previously validated GCCOM, elevating it to field-scale capacity. This reformulation of the GCCOM equations uses novel 3D curvilinear mimetic operators, a buoyancy body force, and mimetic upwind and gradient-based momentum equations developed for this work. This model represents the most complete implementation of the 3D curvilinear mimetic operators utilizing the MOLE library or any other mimetic applications in literature to date. Results show it to be more physically accurate and better energy conserving than the validated GCCOM and other similar models, permitting the use of 3D curvilinear grids for arbitrary geometries, parallelizable arbitrary domain decomposition, and order-of-magnitude wider time steps. Additionally, we implement machine learning models to coastal ocean data to predict Dissolved Oxygen (DO) content with supervised methods; results show a Median Absolute Percentage Error (MAPE) of 2-6% for instantaneous indirect readings of DO and 0.18% for five days forecast of DO in coastal areas, using a previously predicted temperature of 1.60% MAPE. Dissolved Oxygen is known to be a critically important component to track in coastal environments but also expensive to measure and almost impossible to model with traditional methods due to high nonlinearity. The ML component of this thesis opens the possibility of high precision indirect estimates of biogeochemical quantities, along with highly accurate time series forecasts and a host of new applications of machine learning to environmental sciences.