Simulating the ocean’s submesoscale is key to understand the mass and energy cycles of the ocean and the global climate system. Contrast to the ocean’s mesoscale, submesoscale processes are usually highly ageostrophic and manifest at the scales within 10km. Ocean general circulation models with kilometer-resolution are capable to resolve key submesoscale processes, hence indispensable for both process and climate studies. We construct a grid hierarchy for the ocean-sea ice model in the High-Resolution Earth System Model on Sunway supercomputer (SW-HRESM), which is based on Community Earth System Model (CESM2) with deep optimizations on the Chinese home-brew supercomputing architecture of Sunway. The highest grid resolution is 0.03o (2.4km globally). In this study we evaluate the ocean-sea ice coupled simulations by SW-HRESM, focusing on the submesoscale and the kinetic energy (KE) cycles. In particular, highly ageostrophic submesoscale turbulence is simulated, dominated by deepened mixed layers (ML) during winter and the ensuing instabilities. KE and its transition between scales are further evaluated for major western boundary current systems. During winter, submesoscale is shown to dominate inverse cascading which energizes large-scale flows, as well as forward cascading to dissipation scales. The mesoscale-submesoscale continuum and the associated inverse KE cascading is further complemented by the forward KE cascading from the large-scale due to flow instabilities. In order to fully resolve the submesoscale spectrum, including frontal processes and wind-wave interactions, models finer than 1km are needed. Besides the model resolution, improvements for both the ocean and the fully coupled model of SW-HRESM are also discussed.

A four-dimensional ensemble-variational (4DEnVar) data assimilation (DA) system was developed for global numerical weather predictions (NWPs). Instead of using the adjoint technique, this system utilizes a dimension-reduced projection (DRP) technique to minimize the cost function of the standard four-dimensional variational (4DVar) DA. It dynamically predicts ensemble background error covariance (BEC) initialized from its previous inflated analyses and realizes the flow-dependence of BEC in the variational configuration during the assimilation cycle. These inflated analyses, linear combinations of the ensemble analyses increment and balanced random perturbations, aim to prevent the predicted BEC from underestimation as well as to implicitly achieve the hybrid of the flow-dependent and static BEC matrices. A limited number of leading eigenvectors of the localization correlation function are selected to filter out the spurious correlations in the BEC matrix (B-matrix). In order to evaluate the new system, single-point observation experiments (SOEs) and observing system simulation experiments (OSSEs) were conducted with sounding and cloud-derived wind data. The flow-dependent characteristic was verified in the SOEs that utilized the localized ensemble covariance and compared with that of 4DVar. In the OSSEs, 4DEnVar reduced the analysis errors compared with 4DVar. The deterministic forecast initialized from the 4DEnVar ensemble mean analysis has better (worse) performance in the medium-range (long-range) forecasts in the Northern Extratropics and opposite performance in the Southern Extratropics, and exhibits slightly worse effects in the Tropics. Moreover, the ensemble mean forecast initialized from the 4DEnVar ensemble analyses has higher forecast skills than 4DVar.

Climate models contain atmospheric and oceanic components that are coupled together to simulate the thermodynamic and dynamic processes during air-sea interactions. Community Earth System Model (CESM, version 1.2.1) is a state-of-the-art coupled model that is widely used and participates in Coupled Model Intercomparison Projects. Community Atmospheric Model (CAM), the atmospheric component of CESM, is based on the finite-volume dynamic core, which utilizes staggered Arakawa-D grids. However, the dynamics-physics (D-P) coupling in CAM causes the prognostic winds of the dynamic core be interpolated onto non-staggered locations, which affects the wind structure for computing the air-sea interaction and dynamical coupling. In this study we propose a new scheme that eliminates the extra interpolation during D-P coupling for the atmosphere-ocean interaction. By numerical experiments and comparative study of the new scheme, we show that it improves the simulated climatology in key regions including eastern-boundary upwelling regions and Southern Oceans. In turn, existing problems of the model, such as warm SST biases, are reduced. The new scheme contain code changes in CAM and the coupler, and they are provided as open-source files. Similar approaches can also be adopted in coupled models that utilize the atmospheric components with on staggered dynamics and physics, such as spectral-element method based CAM.

This study developed an ensemble four-dimensional variational (En4DVar) hybrid data assimilation (DA) system. Different from most of the available En4DVar systems that adopted ensemble Kalman Filter class or ensemble DA approaches to produce ensemble covariances for their hybrid background error covariances (BECs), it used a four-dimensional ensemble-variational (4DEnVar) system to obtain the ensemble covariance. The localization scheme for 4DEnVar applied orthogonal functions to decompose the correlation matrix so that it was implemented easily and rapidly. In terms of analysis quality and forecast skill, the En4DVar system was evaluated in the single-point observation experiments and observing system simulation experiments (OSSEs) with sounding and cloud-derived wind observations, using its standalone four-dimensional variational (4DVar) and 4DEnVar components as references. The single-point observation experiments visually verified the explicit flow-dependent characteristic of the BEC due to the introduction of the ensemble covariance from the 4DEnVar system. The OSSE-based sensitivity experiments revealed different contributions of the weight for the ensemble covariance in the En4DVar system to the forecasts in the Northern and Southern Extratropics and Tropics. A much higher weight for the ensemble covariance in a properly inflated hybrid covariance helped En4DVar produce the most reasonable analysis. The forecast initialized by En4DVar is overall better than by 4DVar and 4DEnVar, although the quality of En4DVar analysis is between those of 4DVar and 4DEnVar ensemble mean analyses. It indicates that the flow-dependent ensemble covariance provided by 4DEnVar dominantly contributes to the improvements in the En4DVar-initialized forecast, with certain but necessary constraint from the balanced climatological covariance.