Journal Article

A Comparison of Data‐Driven Approaches to Build Low‐Dimensional Ocean Models

Kondrashov, D., Agarwal, Niraj, Ryzhov, E., Dueben, P., Berloff, P.

2021

Overview

We present a comprehensive inter‐comparison of linear regression (LR), stochastic, and deep‐learning approaches for reduced‐order statistical emulation of ocean circulation. The reference data set is provided by an idealized, eddy‐resolving, double‐gyre ocean circulation model. Our goal is to conduct a systematic and comprehensive assessment and comparison of skill, cost, and complexity of statistical models from the three methodological classes. The model based on LR is considered as a baseline. Additionally, we investigate its additive white noise augmentation and a multi‐level stochastic approach, deep‐learning methods, hybrid frameworks (LR plus deep‐learning), and simple stochastic extensions of deep‐learning and hybrid methods. The assessment metrics considered are: root mean squared error, anomaly cross‐correlation, climatology, variance, frequency map, forecast horizon, and computational cost. We found that the multi‐level linear stochastic approach performs the best for both short‐ and long‐timescale forecasts. The deep‐learning hybrid models augmented by additive state‐dependent white noise came second, while their deterministic counterparts failed to reproduce the characteristic frequencies in climate‐range forecasts. Pure deep learning implementations performed worse than LR and its simple white noise augmentation. Skills of LR and its white noise extension were similar on short timescales, but the latter performed better on long timescales, while LR‐only outputs decay to zero for long simulations. Overall, our analysis promotes multi‐level LR stochastic models with memory effects, and hybrid models with linear dynamical core augmented by additive stochastic terms learned via deep learning, as a more practical, accurate, and cost‐effective option for ocean emulation than pure deep‐learning solutions. Plain Language Summary In weather and climate predictions, scientists use comprehensive ocean circulation models for representing the effects of the oceans on the atmosphere. These models simulate the three‐dimensional ocean dynamics using millions of variables and, thus, require significant computational resources and running time. Therefore, there is a need for low‐cost, data‐driven ocean models with fewer variables that can reproduce essential oceanic circulations with reasonable accuracy. There are several popular data‐driven approaches to build these models, but singling out the best one is difficult and significantly understudied. We have systematically assessed and compared the accuracy, stability, and computational cost of various data‐driven models against the linear regression—a fundamental and easy‐to‐implement deterministic model, that is, it provides a fixed output for a fixed input. We considered several stochastic and deep‐learning models for comparison; stochastic models combine a deterministic model with customized noise, whereas deep‐learning models train a complex network of neurons similar to the human brain. We found that the stochastic models that properly include the core dynamics, time‐delay effects, and model errors perform the best. The core dynamics provides the essential changes, time‐delay effects are the changes due to correlation between successive ocean states, and model errors provide other possible causes of changes. Key Points The multi‐level stochastic approach produces the most stable, accurate, and low‐cost emulator of a double‐gyre ocean model solution Artificial neural networks and long short term memory work better in a hybrid form with linear regression, providing the core dynamics, than in their standalone application Emulators incorporating memory effects and state‐dependent noise show enhanced performance and deep learning can learn these effects

• Publisher: John Wiley & Sons, Inc,American Geophysical Union (AGU)
• Subject: Additives / Climatology / data‐driven modeling / Dynamical systems / General circulation models / machine learning / Methods / Neural networks / Noise / Ocean circulation / Ocean circulation models / Ocean models / Oceans / Principal components analysis / reduced order modeling / Statistical models / Stochastic models / Water circulation / Weather forecasting