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

Abstract

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.

Generative Data‐Driven Approaches for Stochastic Subgrid Parameterizations in an Idealized Ocean Model

“…(2021)). One can modify the definition of the subgrid model, for example, by including memory effects, to generate a stochastic model with non‐vanishing energy input (Agarwal et al., 2021; Berner, 2005; Bhouri & Gentine, 2022; Chorin & Lu, 2015; DelSole, 2000; Gagne et al., 2020).…”

“…Wilks (2005) proposed a statistical model of stochastic residuals where free parameters were estimated from the time series of true residuals. Additional works that compare the statistical properties of stochastic 𝐴𝐴 𝐴 𝐴𝐴 and true r residuals include Shutts and Palmer (2007), Arnold et al (2013), Mana and Zanna (2014), Gagne et al (2020), Agarwal et al (2021), and Guillaumin and Zanna (2021).…”

Data‐Driven Stochastic Lie Transport Modeling of the 2D Euler Equations

“…It was found that both parametrizations accurately predict numerical errors and possess good uncertainty skills. The work by Agarwal et al (2021) adopts EOFs and compares several dependent stochastic models and found that models that include the dynamics and time-delay effects perform well.…”

“…The work by Agarwal et al. (2021) adopts EOFs and compares several dependent stochastic models and found that models that include the dynamics and time‐delay effects perform well.…”

Bridging observation, theory and numerical simulation of the ocean using Machine Learning

“…For example, if a model is only trying to represent the surface fields that are most important for the coupling to the atmosphere, the model could focus on the use of the leading principal components (if these can be derived in the presence of coastlines), and learn the interactions between the different components using data from a time-series extracted from long model (or observational) trajectories. However, a first approach towards building low-order ML models using a barotropic model showed that results from DL may not necessarily improve on more classical approaches that combine regression techniques and stochastic forcing [5].…”