We demonstrate the use of information theory metrics, Shannon entropy and mutual information, for measuring internal and forced variability in general circulation coastal and global ocean models. These metrics have been applied on spatially and temporally averaged data. A combined metric reliably delineates intrinsic and extrinsic variability in a wider range of circumstances than previous approaches based on variance ratios that therefore assume Gaussian distributions. Shannon entropy and mutual information manage correlated fields, apply to any distribution, and are insensitive to outliers and a change of units or scale. Different metrics are used to quantify internal vs forced variability in (1) idealized Gaussian and uniformly distributed data, (2) an initial condition ensemble of a realistic coastal ocean model (OSOM), (3) the GFDL-ESM2M climate model large ensemble. A metric based on information theory partly agrees with the traditional variance-based metric and identifies regions where non-linear correlations might exist. Mutual information and Shannon entropy are used to quantify the impact of different boundary forcings in a coastal ocean model ensemble. Information theory enables ranking the potential impacts of improving boundary and forcing conditions across multiple predicted variables with different dimensions. The climate model ensemble application shows how information theory metrics are robust even in a highly skewed probability distribution (Arctic sea surface temperature) resulting from sharply non-linear behavior (freezing point).

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.