Stochastic Deep Learning parameterization of Ocean Momentum Forcing

Abstract

Coupled climate simulations that span several hundred years cannot be run at a high-enough spatial resolution to resolve mesoscale ocean dynamics. These mesoscale dynamics backscatter to macroscales. Recently, several studies have considered Deep Learning to parameterize subgrid forcing within macroscale ocean equations using data from idealized simulations. In this manuscript, we present a stochastic Deep Learning parameterization that is trained on data generated by CM2.6, a highresolution state-of-the-art coupled climate model with nominal resolution 1/10°. We train a Convolutional Neural Network for the subgrid momentum forcing using macroscale surface velocities from a few selected subdomains. At each location and each time step of the coarse grid, rather than predicting a single number, we predict the mean and standard deviation of a Gaussian probability distribution. This approach requires training our neural network to minimize a negative log-likelihood loss function rather than the Mean Square Error, which has been the standard in applications of Deep Learning to the problem of parameterizations. Each prediction of the mean subgrid forcing can be associated with an uncertainty estimate and can form the basis for a stochastic subgrid parameterization. Offline tests show that our parameterization generalizes well to the global oceans, and a climate with increased CO2 levels, without further training. We test our stochastic parameterization in an idealized shallow water model. The implementation is stable and improves some statistics of the flow. Our work demonstrates the potential of combining Deep Learning tools with a probabilistic approach in parameterizing unresolved ocean dynamics.

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

“…Second, the results obtained here are directly relevant for emulation of various complex and multi-scale fields in the context of eddy parameterizations and test the alternative definitions of eddies investigated recently (Agarwal et al, 2021;Berloff et al, 2021). Finally, a possible sequel to this work is including more stochastic and deep-learning methods, or a mixture of both, for example, the Stochastic Neural Networks (Guillaumin & Zanna, 2021). We started to develop a rigorous testbed for data-driven models and used this for several model setups, but we will expand this to more complex testbeds, models, and data sets in the future and check if the conclusions still hold.…”

Diffusion‐Based Smoothers for Spatial Filtering of Gridded Geophysical Data

“…A “top hat” or “boxcar” kernel (i.e., an indicator function over a circle or a square, respectively) is used in all these studies, except for Bolton and Zanna (2019), Stanley, Bachman, et al. (2020), and Guillaumin and Zanna (2021) who used Gaussian kernels. Spatial convolution is not the only way to define or implement spatial filters.…”

“…where E G is the convolution kernel, E  x is a dummy integration variable, and d E  denotes the set of all real vectors of dimension E d. Berloff (2018), Bolton and Zanna (2019), Ryzhov et al (2019), andHaigh et al (2020) all used convolution filters to study subgrid-scale parameterization in the context of quasigeostrophic dynamics in a rectangular Cartesian domain. Lu et al (2016), Aluie et al (2018), Khani et al (2019), Stanley, Bachman, et al (2020), and Guillaumin and Zanna (2021) used approximate spatial convolutions on the sphere to filter ocean general circulation model output, and Aluie (2019) showed how to correctly define convolution on the sphere in such a way that the filter commutes with spatial derivatives. A "top hat" or "boxcar" kernel (i.e., an indicator function over a circle or a square, respectively) is used in all these studies, except for Bolton and Zanna (2019), Stanley, Bachman, et al (2020), and Guillaumin and Zanna (2021) who used Gaussian kernels.…”

“…Lu et al (2016), Aluie et al (2018), Khani et al (2019), Stanley, Bachman, et al (2020), and Guillaumin and Zanna (2021) used approximate spatial convolutions on the sphere to filter ocean general circulation model output, and Aluie (2019) showed how to correctly define convolution on the sphere in such a way that the filter commutes with spatial derivatives. A "top hat" or "boxcar" kernel (i.e., an indicator function over a circle or a square, respectively) is used in all these studies, except for Bolton and Zanna (2019), Stanley, Bachman, et al (2020), and Guillaumin and Zanna (2021) who used Gaussian kernels. Spatial convolution is not the only way to define or implement spatial filters.…”

Diffusion-based smoothers for spatial filtering of gridded geophysical data

“…Lu et al (2016), Aluie et al (2018), Khani et al (2019), Stanley, Bachman, et al (2020), and Guillaumin and Zanna ( 2021) used approximate spatial convolutions on the sphere to filter ocean general circulation model output, and Aluie (2019) showed how to correctly define convolution on the sphere in such a way that the filter commutes with spatial derivatives. A "top hat" or "boxcar" kernel (i.e., an indicator function over a circle or a square, respectively) is used in all these studies, except for Bolton and Zanna (2019), Stanley, Bachman, et al (2020), andGuillaumin andZanna (2021) who used Gaussian kernels. Spatial convolution is not the only way to define or implement spatial filters.…”