Thermal structures at the sea surface are known to affect the overlying atmospheric dynamics over various spatio-temporal scales, from hourly and sub-kilometric to annual and O(1000 km). The relevant mechanisms at play are generally identified by means of correlation coefficients (in space or time) or by linear regression analysis using appropriate couples of variables. For fine spatial scales, where SST gradients get stronger, the advection might disrupt these correlations and, thus, mask the action of such mechanisms, just because of the chosen metrics. For example, at the oceanic sub-mesoscale, around 1-10 km and hourly time scales, the standard metrics used to identify the pressure adjustment mechanism (that involves sea surface temperature, SST, Laplacian and wind divergence) may suffer from this issue, even for weak wind conditions. By exploiting high-resolution realistic numerical simulations with ad hoc SST forcing fields, we introduce some new metrics to evaluate the action of the pressure adjustment atmospheric response to the surface oceanic thermal structures. It is found that the most skillful metrics is based on the wind divergence and SST second spatial derivative evaluated in the across direction of a locally defined background wind field.