Parameterizing Submesoscale Vertical Buoyancy Flux by Simultaneously Considering Baroclinic Instability and Strain-Induced Frontogenesis

Oceanic submesoscale processes (submesoscales) with O(1-10) km horizontal scale can generate strong vertical buoyancy flux (VBF) that significantly modulate upper-ocean stratification. Because submesoscales cannot be resolved by the prevailing ocean models, their VBFs have to be properly parameterized in order to improve model performance. Here, based on theoretical scaling analysis, we propose a new parameterization of submesoscale VBF by simultaneously considering mixed-layer baroclinic instability (MLI) and strain-induced frontogenesis, which are two leading generation mechanisms of submesoscales that typically co-occur in open ocean. Compared with the parameterization of Fox-Kemper et al. (2008, ; F08) that only considers the MLI, the new parameterization includes mesoscale strain rate and improves vertical structure function. Diagnostic validations based on submesoscale permitting simulation outputs suggest that the newly parameterized VBFs are more realistic than F08 in regard to three-dimension distributions. How to incorporate this new parameterization into coarser-grid ocean models, however, needs further studies.Plain Language Summary Oceanic submesoscale processes with spatial scale of O(1-10 km) can generate strong vertical buoyancy flux (VBF) in upper ocean and therefore, they significantly modulate the vertical density distribution (i.e., stratification). Because the prevailing ocean circulation models typically have horizontal resolutions of O(10-100 km), they are unable to resolve the submesoscale VBF. In order to accurately simulate the upper-ocean stratification, the unresolved VBF needs to be expressed using the resolved larger-scale quantities, which is called parameterization. Here, based on theoretical scaling analysis, we propose a new parameterization of submesoscale VBF by simultaneously considering contributions from mixed-layer instability (MLI; baroclinic instability occurring in the mixed layer) and front sharpening induced by mesoscale strain, which are two important generation mechanisms of submesoscales. Compared with the previous parameterization by Fox-Kemper et al. (2008, https://doi.org/10.1175/2007jpo3792.1; F08) that only includes MLI mechanism, the new parameterization has incorporated mesoscale strain rate and improved vertical structure function more realistically. Diagnostic analysis based on high-resolution simulation outputs demonstrates that the newly parameterized VBFs are more realistic in aspect of both horizontal and vertical distributions than the F08 parameterization. The test and application of this parameterization in ocean models will be a focus of future studies.