A new stochastic ocean physics package and its application to hybrid-covariance data assimilation

Generating optimal perturbations is a key requirement of several data assimilation schemes. Here, we present a newly developed stochastic physics package for ocean models, implemented in the NEMO ocean general circulation model. The package includes three schemes applied simultaneously: stochastically perturbed parametrization tendencies (SPPT), stochastically perturbed parameters (SPP) and stochastic kinetic energy backscatter (SKEB) schemes. The three schemes allow for different temporal and spatial perturbation scales. Within a limited-area ocean model configuration, ensemble free-running simulations were performed to assess the impact and reliability of the schemes. They prove complementary in increasing the ensemble spread at different scales and for different diagnostics. The ensemble spread appears reliable; for instance, it proves consistent with the root-mean-square differences with respect to higher-resolution (sub-mesoscale) simulations that here represent the "truth" (in the sense that it includes "unresolved physics"). Interestingly, both the SPPT and the SKEB schemes lead to an increase of eddy kinetic energy at small spatial scales (2-10 km), and contribute to modify the ensemble mean state, mitigating warm biases near the thermocline due to the enhancement of the upper ocean vertical mixing. As an application of the stochastic packages, the ensemble anomaly covariances coming from the ensemble free-running simulations are used to feed large-scale anisotropic covariances that complement smaller-scale ones in a hybrid-covariance regional analysis and forecast system in the Mediterranean Sea. Ensemble-derived covariances are formulated as slowly varying three-dimensional low-resolution empirical orthogonal functions (EOFs). The improvements due to the addition of such covariances to the stationary ones are found significant in real-data experiments, within verification skill scores against glider profile data, remotely sensed observations and current speed measurements from drifters, radar and moorings.