Surface Quasigeostrophic Solutions and Baroclinic Modes with Exponential Stratification

Abstract

Abstract The author derives baroclinic modes and surface quasigeostrophic (SQG) solutions with exponential stratification and compares the results to those obtained with constant stratification. The SQG solutions with exponential stratification decay more rapidly in the vertical and have weaker near-surface velocities. This then compounds the previously noted problem that SQG underpredicts the velocities associated with a given surface density anomaly. The author also examines how the SQG solutions project onto the baroclinic modes. With constant stratification, SQG waves larger than deformation scale project primarily onto the barotropic mode and to a lesser degree onto the first baroclinic mode. However, with exponential stratification, the largest projection is on the first baroclinic mode. The effect is even more pronounced over rough bottom topography. Therefore, large-scale SQG waves will look like the first baroclinic mode and vice versa, with realistic stratification.