Fig. 4: Relationship between the rate of frontal sharpening and horizontal convergence across horizontal scales.

Scatter plots of the daily-averaged normalized frontogenetic rate Tb/f and the normalized horizontal convergence − δ/f in winter, estimated at horizontal scales of (a) 18 km, (b) 9 km and (c) 2 km for all observed depths. The correlation coefficient R2 and p-value are indicated, and illustrate the agreement with the submesoscale frontogenesis theory of Barkan et al. (2019)13 at finer horizontal scales.