Towards a Unified Data-Driven Boundary Layer Momentum Flux Parameterization for Ocean and Atmosphere

TL;DR

The paper addresses the challenge of accurately parameterizing subgrid momentum flux in both atmospheric and oceanic boundary layers by introducing a unified data-driven ANN trained on coarse-grained LES data. By normalizing vertical flux profiles by their surface values, the authors uncover a self-similar, cross-fluid structure that enables joint training and robust generalization across regimes, including upgradient fluxes that traditional closures miss. Online tests in SCAM show the ANN outperforming CLUBB, especially in convective conditions, with resistance to surface-flux biases and strong cross-fluid transfer when augmented with atmospheric data. The work highlights the potential of a unified, physics-informed machine-learning approach to improve climate-model representations of boundary-layer turbulence and motivates further validation in fully coupled Earth system models.

Abstract

Boundary layer turbulence, particularly the vertical fluxes of momentum, shapes the evolution of winds and currents and plays a critical role in weather, climate, and biogeochemical processes. In this work, a unified, data-driven parameterization of turbulent momentum fluxes is introduced for both the oceanic and atmospheric convective boundary layers. An artificial neural network (ANN) is trained offline on coarse-grained large-eddy simulation (LES) data representing a wide range of turbulent regimes in both fluids. By normalizing momentum flux profiles with their surface values, we exploit a self-similar structure across regimes and fluids, enabling joint training. The ANN learns to predict vertical profiles of subgrid momentum fluxes from mean wind or current profiles, capturing key physical features such as upgradient fluxes that are inaccessible to traditional first-order closure schemes. When implemented online in the Single Column Atmospheric Model (SCAM), the ANN parameterization consistently outperforms the SCAM baseline parameterization in replicating the evolution of the boundary layer wind profiles from the LES, especially under convective conditions, with errors reduced by a factor of 2-3 across regimes. ANN performance remains robust even when the surface momentum flux is biased up to 30\%, and generalization is confirmed by testing on LES cases excluded from the training dataset. This work demonstrates the potential of machine learning to create unified and physically consistent parameterizations across boundary layer systems in climate models.

Figures (7)

• Figure 1: Vertical profiles of turbulent momentum fluxes computed from the atmospheric LES (a and b) and oceanic LES (e and f). The fluxes normalized by their surface value are shown in panels c, d, g and h. The common vertical levels used for joint training are labeled as vertical level indices. Each thick line represents the average flux from a single LES simulation, noted as $\zeta_x$, with $x$ being the stability parameter of the corresponding run. The shaded area corresponds to the flux standard deviation of the simulation. The atmospheric vertical profiles have been interpolated on the SCAM momentum levels. The oceanic vertical profiles have been interpolated on the same number of vertical levels, evenly spaced. The ocean fluxes have also been flipped in the normalization process in order to match the shape of the atmospheric fluxes.
• Figure 2: Offline predictions of the testing set. The testing samples were split between the atmospheric (left) and oceanic (right) features. The top panels (a,b, d, e) show the average true vertical profiles of momentum fluxes in $m^2/s^2$(orange thick lines) and average ANN predictions (thick blue lines). The shaded areas correspond to the standard deviations of the samples. The unnormalized fluxes are shown here. The bottom panels (c, f) show the density plots of predicted versus true fluxes, the values at each vertical level is considered for every test sample.
• Figure 3: Upgradient momentum fluxes from the testing set. Two different samples of mean zonal wind (a) and current (c) are shown, as well as the corresponding momentum fluxes (b, d, thick orange lines) computed from the LES. The ANN-predicted momentum fluxes are also shown (b, d, thick blue lines). The gray shaded areas represent the parts of the boundary layers where the fluxes are upgradient.
• Figure 4: Improvement of the normalized RMSE after inclusion of atmospheric samples, in an ocean-data limited regime. A first ANN is trained using 100 oceanic samples randomly picked in one of the twelve LES runs, and tested on a different set of 100 oceanic samples after computing the prediction RMSE (blue diamonds). The testing samples are randomly picked in the remaining eleven LES runs. A second ANN is trained from scratch after adding 1000 atmospheric samples to the initial training set, and tested on the same initial testing set (green diamonds). The uncertainty induced by the random weight initialization of the ANN is computed by training ten separate ANNs with the same samples, and computing the mean (diamonds) and standard deviations (error bars) of the normalized RMSE. The operation is repeated for the twelve LES runs. Here, the oceanic samples change at each iteration (in both the training and testing set), but the added 1000 atmospheric samples are kept unchanged.
• Figure 5: Stability parameters (top panel) and parameterization errors (bottom panel) for all of the fifteen replicated LES runs. The run names on the x axis correspond to the values of geostrophic wind forcing $Ug$ and surface heating $Q$ used in the simulations, and are classified in increasing order of convective strength from left to right. The error metric used is the normalized distance between the wind vectors simulated by SCAM and the LES wind vectors, averaged over every vertical levels and time steps. The blue and yellow dots correspond to the average error computed after running SCAM with the ANN parameterizations, with the replicated LES included and removed from training, respectively. The brown dots correspond to the average error of the baseline parameterization CLUBB. The small transparent dots show the errors computed after applying biases (ranging from -30% to +30%) to the surface flux values during the SCAM runs.