Accurate sea ice models are essential to predict the complex evolution of rapidly changing sea ice conditions and study impacts on climate, wildlife, and navigation. However, numerical models for sea ice contain various uncertainties associated with initial conditions and forcing (wind, ocean), as well as with parameter values and parameterizations, functional forms of the constitutive relations, and state variables such as sea ice thickness and concentration, all of which limit predictive capabilities. In this work, we first develop new stochastic partial differential equation (PDE)-based Sea Ice Dynamically Orthogonal equations and schemes for efficient uncertainty propagation and probabilistic predictions. These equations and schemes preserve nonlinearities in the underlying spatiotemporal dynamics and evolve the non-Gaussianity of the statistics with a lower computational cost than Monte Carlo methods commonly used in sea ice data assimilation and sensitivity analysis. We then use the Gaussian Mixture Model (GMM)-DO filter for sea ice Bayesian nonlinear data assimilation and learning. Assimilating noisy and sparse measurements, we provide posterior probability distributions for not only the sea ice velocities, thickness, and concentration, but also for the external forcing, parameters, and even functional forms of the sea ice model. The equations and schemes are evaluated using stochastic test cases, in which we showcase the ability to evolve non-Gaussian statistics and capture complex nonlinear dynamics efficiently. We demonstrate the stochastic convergence of the probabilistic predictions to the stochastic subspace size and coefficient samples. Finally, we highlight the principled joint nonlinear inference and learning of the sea ice state and dynamics.

In the Gulf of Mexico, the Loop Current (LC) is a salient oceanographic feature, being a warm-water current originating from the Caribbean Sea, traveling northward, protruding into the Gulf, and eventually departing through the Florida Strait. This dynamic stream influences the intensity of hurricanes, the vitality of coastal and estuarine ecosystems, the efficiency of petroleum exploration and extraction, and the prosperity of the fishing sector. These intricacies, in turn, profoundly affect the region’s overall economic framework. Given its overarching impact, the compelling question arises: How can we accurately forecast the likelihood of future Loop Current phenomena and anticipate the evolving oceanic conditions within the Gulf? We develop and utilize differential Dynamical-Orthogonal primitive-equations (DO-PEs) for efficient and high-resolution stochastic ocean forecasting in regions with complex ocean dynamics. We can then perform the equivalent of massive ensemble simulations of 10⁶ members in a stochastic subspace while ensuring that the initial statistics respect the physical processes, modeled complex dynamics, and uncertainty in initial conditions of the Gulf of Mexico. We demonstrate the convergence of DO probabilistic forecasts as the number of modes increases, effectively replicating full-order Monte Carlo ensemble simulations. Our analysis quantifies predictability boundaries, predictive capacities, and variability from initial and boundary conditions. Additionally, we formulate ensemble hindcasts for varying periods and LC states. We complete some targeted multi-resolution modeling experiments. We also compute Mutual Information (MI) and correlation fields to determine the most informative observations and their impacts on ocean predictions. Ultimately, our work can be used to provide rich probabilistic forecasts and inform the design of shorter- and longer-term observing campaigns.

Regional three-dimensional pathways of water parcels from the surface to the ocean interior are investigated in a high-resolution realistic model simulation of the Western Mediterranean Sea. This simulation assimilates multi-platform observations from both satellite and in-situ measurements collected during the ONR CALYPSO experiment carried out north of the Balearic Islands in Winter-Spring 2022. This experiment provided high-resolution observations of temperature, salinity, currents, oxygen and chlorophyll fluorescence using eight gliders, several towed CTD instruments, Lagrangian floats, and more than 300 Lagrangian drifters. These observations are used here to constrain a 2km-resolution model reanalysis spanning a 5-month period from February to June 2022. Three-dimensional water pathways were then computed to characterize the path of parcels at different time scales in the model domain. An independent comparison against specific observations identifying patterns of subduction was performed, showing the realism of the simulated paths. A free-run nested simulation with 650m resolution was also implemented in a reduced area to evaluate the impact of the finer-scale features. The spatial and temporal variability of the vertical pathways are described and linked to the meso- and submesoscale ocean structures represented in the simulation. This numerical approach allowed us to map areas of subduction, evaluate their temporal evolution, quantify the export of surface parcels to depth, and obtain a first estimate of the relative contribution of mesoscale and submesocale ocean features to the vertical transports.

In the winter/spring of 2022, the CALYPSO DRI team carried out an intensive multi-platform field experiment to investigate the three-dimensional subduction pathways in the Balearic Sea. As part of this effort, we provided real-time, high-resolution, multiscale deterministic and ensemble forecasts utilizing the Multidisciplinary Simulation, Estimation, and Assimilation System Primitive Equation model (MSEAS-PE) configured for 900 m and 300 m stand-alone and nested configurations. The forecasts were downscaled from the larger WMOP western Mediterranean forecasts. Probabilistic forecasts (200-300 members) were made using the Error Subspace Statistical Estimation (ESSE) system. The skill of these forecasts was assessed by comparison with independent in situ data, satellite data, and drifter tracks using bias and RMSE metrics and by comparison with features using qualitative and quantitative analyses. The 3D subduction pathways were diagnosed using a combination of flow maps, finite-time Lyapunov exponents, dilation maps, and 3D subduction maps computed from the flow maps. During the experiment, we used Gaussian Mixture Models (GMM) and Dynamically Orthogonal (DO) ensemble filters to assimilate the Lagrangian surface drifter position data in real-time, which improved the RMSE comparison to T/S data by 13% in the upper 150m. Follow-on reanalyses further improve the comparisons to data and are used to explore and diagnose the 3D subduction dynamics.

Strong mesoscale and submesoscale features are characterized by Rossby and Richardson numbers close to one, indicating that geostrophic balance breaks down. This gives rise to the development of ageostrophic flows that create a circulation across density gradients, with vertical motions associated. These vertical fluxes transport carbon and other biogeochemical tracers from the surface layer to depths below the mixed layer. In the Western Mediterranean Sea during winter 2022, the ONR CALYPSO experiment employed a multidisciplinary approach to observe and predict the ocean fields in the Balearic Sea (BalS), combining multiplatform in-situ observations with high-resolution realistic numerical simulations. The results showed strong mesoscale and submesoscale fields where structures interact, exchange energy, and are affected by wind forcing. We observed a mesoscale front (BalSF) associated with a mesoscale vortex dipole (MVD). As it evolved, the front cascaded to smaller scales, forming a mesoscale ridge (MR) and submesoscale cyclones (SCs). This work analyzes the evolution and interaction of the BalSF, MVD, MR, and SCs using numerical simulations with 2000 m and 650 m horizontal resolution, respectively. We employ spatial filtering of our simulations to extract and diagnose energy exchanges between mesoscale and submesoscale features. The BalSF and MVD evolutions are explained through i) intensification by frontogenesis, ii) favorable conditions for overturning instabilities, indicating the beginning of the front’s collapsing, and iii) nonlinear Ekman subduction produced by a strong wind event. The formation of MR and SCs structures was associated with frontal variability and driven by a combination of barotropic and baroclinic processes that are responsible for the eddy kinetic energy generation. Particle tracking analysis indicates that subduction areas are located in thin threads of strong cyclonic vorticity embedded in a weak anticyclonic background.