Why is the Westward Rossby Wave Propagation from the California Coast “Too Fast”?

Past work has shown that interannual California coastal sea level variability is mostly of equatorial origin, and decades of satellite sea surface height (SSH) and in situ dynamic height observations indicate that this interannual signal propagates westward from the California coast as nondispersive Rossby waves (RWs). These observations agree with standard linear vertical mode theory except that even when mean flow and bottom topography are considered, the fastest baroclinic vertical mode RW in each case is always much slower (1.6 – 2.3 cm/s) than the observed 4.2 cm/s. This order one disagreement is only resolved if the standard bottom boundary condition that the vertical velocity w′ = 0 is replaced by perturbation pressure p′ = 0. Zero p′ is an appropriate bottom boundary condition because south of San Francisco the northeastern Pacific Ocean boundary acts approximately like an impermeable vertical wall to the interannual equatorial wave signal, and therefore equatorial quasi-geostrophic p′ is horizontally constant along the boundary. Thus if equatorial p′ = 0 at the bottom, then this condition also applies off California. The large-scale equatorial ocean boundary signal is due to wind-forced eastward group velocity equatorial Kelvin waves, which at interannual and lower frequencies propagate at such a shallow angle to the horizontal that none of the baroclinic equatorial Kelvin wave signal reaches the ocean floor before striking the eastern Pacific boundary. Off California this signal can thus be approximated by a first baroclinic mode with p′ = 0 at the bottom, and hence the long RW speed there agrees with that observed (both approximately 4.2 cm/s).