Source-linked AI summary
Developing an Offshore Machine Learning Surface Layer Scheme
Susan Dettling, Sue Ellen Haupt, Thomas Brummet, Patrick Hawbecker, Branko Kosović, David John Gagne
TL;DR
Surface-layer models use empirically fitted relationships, motivating machine-learning improvements for flux processes. This work develops and evaluates machine-learning surface-layer models using measurements from three sites; the models captured flux-calculation scales better than MOST and continued to outperform MOST when transferred between sites.
Problem
Surface-layer models rely on empirically fitted coefficients relating variables, motivating improved machine-learning models for flux processes.
Method
The study develops machine-learning surface-layer models from flux measurements in marine environments and evaluates them across three measurement sites.
Results
Both neural-network and random-forest models captured the scales underlying flux calculations better than MOST at both sites and outperformed MOST when transferred between sites.
Takeaways & Limitations
Machine-learning models can improve representation of surface flux scales beyond MOST, including when models are applied across measurement sites.
Takeaways & Limitations
The comparison includes a scheme focused on flat to gently rolling grassland, limiting its environmental scope relative to marine applications.
Abstract
from arXiv · showhide
Turbulent fluxes between the surface and the atmosphere are typically parameterized using empirically fit relationships. Here we test machine learning techniques for fitting the relationship for the offshore environment. To do that, data from three offshore sites are used: the Martha's Vineyard Coastal Observatory (MVCO) air-sea interaction tower, the FINO1 research platform, and the CASPER-West FLIP research vessel deployed off the coast of California. Two machine learning methods were employed: Neural Networks (NN) and Random Forests (RF). Because the observational sites had towers with measurements at different levels, the vertical differences were input as gradients. Models were built for both momentum flux and heat flux. ML models trained at the individual sites were competitive with and in some cases, better than the physically-based COARE-3 model tailored to offshore fluxes. The heat flux ML models generally outperformed the physics-based parameterizations for most metrics, but the results were mixed for momentum flux, with only the site with the most training data (MVCO) producing results better than COARE-3. When the ML models from that site were applied to the other sites, results were degraded from using data from the site being tested. ML models built from data combined from the three sites generally showed improvements for the sites with less available training data. When assessing which variables were most important, the wind speed was most important for momentum flux and temperature gradient for heat flux.
1. Introduction
Surface-layer flux models commonly rely on empirical coefficients developed for land environments, motivating offshore machine-learning parameterizations built from marine observations and compared with MOST and COARE.
- Motivation: MOST-based surface-layer formulations use empirical coefficients that are often applied globally despite originating from grassland experiments.The paper notes that these formulations also assume horizontal homogeneity and stationarity, assumptions seldom met in practice.
- Motivation: Machine learning is attractive because it can leverage surface-flux observations more directly than empirically fitted parameterizations.
- Prior work: Prior land-based studies found neural networks and random forests captured flux-related scales better than MOST at two sites.
- Prior work: Models trained at one land site still outperformed MOST when applied to another site, indicating cross-site transferability in those tests.
- Study goals: This study develops an offshore machine-learning surface-layer model using three marine measurement sites and evaluates it against MOST and COARE.
- Study goals: A companion study evaluates implementation of the resulting models in WRF and their application to coastal environments.
2. Approach – Data and Methods
The paper frames offshore flux prediction around MOST and COARE parameterizations, whose roughness and stability relationships provide the physical baselines for machine-learning models.
- Physical baselines: MOST underpins bulk parameterizations of surface exchange coefficients in numerical weather prediction models.
- Study rationale: The study uses these physically based formulations as comparison points for machine-learning surface-flux parameterizations.
- Physical baselines: COARE represents momentum and scalar roughness using relationships involving friction velocity, wind speed, stability, and roughness Reynolds number.
- Physical baselines: COARE improves on earlier roughness formulations through field-based parameterizations for air–sea exchange.
2) IMPLEMENTATION
The implementation combines physically relevant offshore observations from three sites with COARE-based flux estimation and machine-learning inputs designed for cross-site use.
- Baseline model: COAREv3 estimates momentum, sensible-heat, and latent-heat fluxes from atmospheric and surface-state variables while iteratively solving stability parameters.
- Datasets: The study develops machine-learning models from three datasets containing atmospheric, ocean-state, and near-surface momentum and heat-flux measurements.
- Predictors: Common predictors include wind speed, temperature, humidity, pressure, sea-surface temperature, wave height, and wave phase speed.
3) MVCO ASIT
MVCO supplies a long offshore record for model development, with quality-controlled observations, cross-validation, and an independent holdout evaluation.
- Data: MVCO observations come from the ASIT tower south of Martha’s Vineyard, using data from 2006 through 2016.
- Data limitations: Several months of MVCO data were missing or excluded during quality control.
- Data: The model uses meteorological variables from the lowest ASIT flux-measurement level at 18.4 m, averaged over 20-minute intervals.
- Data: 53,278 MVCO samples remained after quality control, substantially more than were available from the other two datasets.
- Evaluation: MVCO uses five-fold cross-validation, while the smaller FINO and CASPER datasets use ten-fold cross-validation.
- Evaluation: Approximately 85–87% of available data supports model development through cross-validation, with an independent holdout set reserved for final testing.
- Predictors: Predictors include wind, humidity, pressure, sea-surface temperature, wave characteristics, the Bulk Richardson Number, and vertical gradients.
2) NEURAL NETWORK
The models use configurable neural networks and random forests, with Bayesian optimization and iterative predictor selection to fit offshore fluxes while accounting for inter-site imbalance.
- Neural networks use fully connected hidden layers, nonlinear activations, and a final linear regression output layer.
- Adam optimization, validation-based early stopping, normalized inputs and targets, and optional sample weighting were used during training.Sample weights addressed unequal representation among sites.
- Bayesian optimization and permutation-based importance testing jointly refined hyperparameters and the physically relevant predictor set.The two-stage process repeated optimization after reducing predictors.
- Across datasets and flux types, selected predictors included wind speed, velocity and temperature gradients, ocean state, and thermodynamic variables.
- Random Forest effective tree depth varied with data characteristics, with deeper trees for MVCO and combined datasets and shallower trees for FINO and CASPER.Mean depths were approximately 37–42 for MVCO and combined datasets versus 25–26 for FINO and CASPER.
- For CASPER momentum flux, constraining maximum tree depth to 20 was associated with improved generalization in the data-limited regime.All trees reached the depth-20 limit.
- Site weighting assigned approximately 0.25, 1.05, and 1.85 to MVCO, FINO, and FLIP observations, respectively.The weighting reduced sampling imbalance while retaining all observations.
- Evaluation used RMSE, MAE, Pearson correlation, and Wasserstein distance, for which smaller values indicate better results.
3. Results
The results evaluate site-specific models, transfer of MVCO models to other sites, combined-site training, and variable importance across the three offshore datasets.
- RF and NN models were developed, optimized, and tested separately for each individual site despite unequal training and testing data.
- MVCO models were applied to FINO and CASPER to assess whether models trained at the largest site could transfer.
- Data from all sites were combined to produce models evaluated separately on each site, alongside variable-importance analysis and testing of the derived B Ri variable.
a. Site Specific Results
Site-specific ML models were competitive with physics-based methods, especially for heat flux, but momentum-flux performance varied by site, metric, and model type.
- Momentum flux: At MVCO and FINO, ML models led momentum-flux MAE, RMSE, and Pearson correlation metrics, except COARE-3 had the lowest FINO MAE.
- Momentum flux: At CASPER, COARE-3 was optimal for momentum flux, the site with the least data for training ML algorithms.
- Momentum flux: Wasserstein-distance winners varied by site: MOST at MVCO, NN at FINO, and COARE-3 at CASPER.
- Heat flux: For heat flux, ML models outperformed physics-based parameterizations across sites for RMSE, MAE, and Wasserstein distance, while MOST had the highest CASPER correlation.
- Heat flux: NN and RF heat-flux performance was comparable at MVCO and FINO, while RF outperformed NN at CASPER.
- Cross-site transfer: For transferred momentum-flux models, RF performed better for RMSE, MAE, and Wasserstein distance, while NN had better CASPER correlation.
- Cross-site transfer: Applying MVCO models to other sites degraded momentum-flux metrics relative to models trained on each specific site.
- Cross-site transfer: Transferred heat-flux models beat MOST or COARE-3 on FINO for RF RMSE and MAE, whereas COARE-3 remained strongest on CASPER except for correlation.
3) COMBINED DATA FLUX ESTIMATES
Combining data across sites benefited heat-flux prediction at the smallest-data site, while momentum-flux gains were mixed and model-dependent.
- Momentum flux: For momentum flux, both physics-based and ML models performed well, with COARE-3 outperforming them in the reported comparison.
- Momentum flux: Combined-site training improved NN momentum-flux pointwise metrics at FINO and yielded gains for CASPER, especially RMSE, but degraded all MVCO metrics.
- Momentum flux: RF momentum-flux models showed mixed combined-training effects, with minor gains in selected metrics and no overall improvement pattern.
- Momentum flux: Momentum flux was often predictable from local conditions alone, with limited and model-dependent gains from cross-site training data.
- Heat flux: Combined training improved CASPER heat-flux performance across all metrics, while NN changes at FINO and MVCO were modest or metric-dependent.
- Heat flux: RF heat-flux performance generally degraded at FINO and CASPER under combined training, indicating greater sensitivity to cross-site heterogeneity.
- Heat flux: For combined heat-flux training, NN was best overall and both NN and RF beat MOST and COARE-3.
d. Relative importance of variables and derived variables
Variable importance differed by flux type: wind speed dominated momentum-flux prediction, while temperature gradient dominated heat-flux prediction. Bulk Richardson number generally added little, with small and inconsistent performance changes when included.
- Variable importance: Wind speed was the most important variable for momentum-flux prediction in both neural-network and random-forest models.
- Variable importance: For combined heat-flux models, random forests ranked wind-speed gradient and temperature gradient next, followed by moisture gradient, Bulk Richardson number, sea-surface temperature, and wave height.
- Variable importance: Temperature gradient was the most important heat-flux predictor for both model types by a large margin, followed by wind-related and moisture variables.
- Variable importance: For combined momentum-flux models, neural networks ranked wave height and relative humidity next, whereas random forests emphasized Bulk Richardson number and sea-surface temperature.
- Derived variables: Removing Bulk Richardson number produced small and inconsistent metric differences across sites and model types, with no Pearson-correlation change reported for MVCO.
- Derived variables: The models appeared to use raw wind and moisture gradients to identify stability information, although explicit Bulk Richardson number inclusion sometimes improved results.
Data Availability Statement.
The study used data from three offshore sites, with MVCO data downloaded from its historical webpage and FINO and CASPER-West data obtained from referenced authors.
- MVCO data were downloaded from the MVCO Historical Data webpage in March 2025.
- FINO and CASPER-West data were obtained by request from the authors referenced for those sites.
APPENDIX
The appendix provides the hyperparameter settings used for the machine-learning models, including optimized settings for heat-flux and momentum-flux models.
- The appendix includes hyperparameter settings for the machine-learning models.
- Table A1 lists optimized hyperparameter settings for heat flux.
- Table A2 lists optimized hyperparameter settings for momentum flux.