Predicting Ocean Turbulence across Orders of Magnitude Using Neural Networks Trained on Multiyear Observations

Abstract Turbulence quantities in geophysical fluids roughly follow a lognormal distribution. Consequently, extreme values dominate arithmetic means, and it is challenging for regression algorithms to accurately predict point-to-point and mean values. We train neural networks (NNs) to predict logarithmic values of turbulence diffusivity K T from multiyear observational records of turbulence in the deep-cycle layer (DCL) of the upper ocean at Earth’s equator, with the objective of accurately predicting long-term statistics of K T . Depending on prescribed input variables, temporal averaging, and the number of internal parameters N nn , NNs can predict instantaneous values of log 10 K T with correlation coefficients R as high as 0.6–0.65, root-mean-square error less than an order of magnitude, and long-term averages of K T within a factor of 2 between predictions and observations. Prescribing small N nn compared to the training dataset size results in poor representation of the distribution’s tails. Conversely, prescribing large N nn causes overfitting degrading the instantaneous predictability. NNs reproduce the observed spread in K T of multiple orders of magnitude at given gradient Richardson number Ri, unlike commonly used physics-based parameterizations which are single-valued functions of Ri. Predictions of the log 10 of vertical turbulent heat flux J q are qualitatively similar to those of log 10 K T but with poorer correlation because of differences between the observed distributions. Tests for spatial generalizability show that when training on two of three equatorial locations, each having DCLs, with multiyear records (140°, 23°, and 10°W), predictions at the third location are less accurate than when training from the same site. Significance Statement By enhancing thermodynamic mixing, ocean turbulence transports heat from the surface to the ocean interior. Directly quantifying this transport requires careful, small-scale, long-term observations. Since such observations are rare in both space and time, it is necessary to infer turbulence parameters from conventional measurements like temperature or current velocity. Machine learning predictive algorithms, trained using existing long-term observations, show promise as a means to achieve this goal. A challenge to overcome is how to characterize the lognormal-like distribution of turbulence levels, in which values vary over orders of magnitude and a few extreme values dominate the arithmetic mean. Reproducing this distribution with neural networks is not trivial, and identifying how to do so is a focus of this paper.