We propose a metric for measuring internal and forced variability in ensemble atmosphere, ocean, or climate models using information theory: Shannon entropy and mutual information. This metric differs from the standard ensemble-variance approaches. Information entropy quantifies variability by the size of the visited probability distribution, as opposed to variance that measures only its second moment. Shannon entropy and mutual information manage correlated fields, apply to any data, and are insensitive to outliers as well as a change of units or scale. Finally, we use an example featuring a highly skewed probability distribution (Arctic sea surface temperature) to show that the new metric is robust even with a sharp nonlinear cutoff (the freezing point). We apply these two metrics to quantify internal vs forced variability in (1) idealized Gaussian data, (2) an initial condition ensemble of a realistic coastal ocean model, (3) the Community Earth System Model large ensemble. Each case illustrates the advantages of the proposed metric over variance-based metrics. Furthermore, in the coastal ocean model, the new metric is adapted to further quantify the impact of different boundary forcing choices to aid in prioritizing model improvements–i.e., comparing different choices of extrinsic forcing. The metric can be applied to any ensemble of models where intrinsic and extrinsic factors compete to control variability and can be applied regardless of if the ensemble spread is Gaussian.

Energy is transferred from the atmosphere to the ocean primarily through ocean surface waves and the majority is dissipated locally in the near-surface ocean. Observations of turbulent kinetic energy (TKE) in the upper ocean have shown dissipation rates exceeding law-of-the-wall theory by an order of magnitude. The excess near-surface ocean TKE dissipation rate is thought to be driven primarily by wave breaking, which limits wave growth and transfers energy from the surface wave field to the wave-affected layer of the ocean. Here, the statistical properties of breaking wave dynamics in a coastal area are extracted from visible imagery and used to estimate TKE dissipation rates due to breaking waves. The statistical properties of whitecap dynamics are quantified with Λ(c), a distribution of total whitecap crest length per unit area as a function of crest speed, and used to compute energy dissipation by breaking waves, Sds. Sds approximately balances elevated subsurface dissipation in young seas, but accounts for only a fraction of subsurface dissipation in older seas. The wind energy input is estimated from wave spectra from polarimetric imagery and laser altimetry. Sds balances the wind energy input except under high winds. Λ(c)-derived estimates of TKE dissipation rates by breaking waves compare well with the atmospheric deficit in TKE dissipation, a measure of energy input to the wave field (Cifuentes-Lorenzen et al., 2024). These results tie the observed atmospheric dissipation deficit and enhancement in subsurface TKE dissipation to wave driven energy transport, constraining the TKE dissipation budget near the air-sea interface.

The Ocean State Ocean Model OSOM is an application of the Regional Ocean Modeling System spanning the Rhode Island waterways, including Narragansett Bay, Mt. Hope Bay, larger rivers, and the Block Island Shelf circulation from Long Island to Nantucket. This paper discusses the physical aspects of the estuary (Narragansett and Mount Hope Bays and larger rivers) to evaluate physical circulation predictability. This estimate is intended to help decide if a forecast and prediction system is warranted, to prepare for coupling with biogeochemistry and fisheries models with widely disparate timescales, and to find the spin-up time needed to establish the climatological circulation of the region. Perturbed initial condition ensemble simulations are combined with metrics from information theory to quantify the predictability of the OSOM forecast system–i.e., how long anomalies from different initial conditions persist. The predictability timescale in this model agrees with readily estimable timescales such as the freshwater flushing timescale evaluated using the total exchange flow (TEF) framework, indicating that the estuarine dynamics rather than chaotic transport is the dominant model behavior limiting predictions. The predictability of the OSOM is ~ 7 to 40 days, varying with parameters, region, and season.