Effects of geographic variation in vertical mode structure on the sea surface topography, energy, and wind forcing of baroclinic Rossby waves

Interpretation of sea surface height anomaly (SSHA) and wind forcing of first baroclinic mode Rossby waves is considered using linear inviscid long-wave dynamics for both the standard and surface-intensified vertical mode in a continuously stratified rest-state ocean. The ratio between SSHA variance and vertically integrated energy of waves is proportional to 1) a dimensionless ratio characterizing the surface intensification of the pressure eigenfunction, 2) the squared internal gravity wave speed, and 3) the inverse of the water depth. Geographic variations in stratification and bathymetry can therefore cause geographically varying SSHA variance even for spatially uniform wave energy. The ratio between SSHA variance and wave energy across the North Atlantic shows important spatial variations based on eigensolutions for the standard vertical mode determined numerically using climatological hydrography. The surface-intensified mode result is similar, though the ratio is generally slightly larger and less sensitive to depth variations. Results are applied to the propagating annual-frequency portion of TOPEX altimeter SSHA in the North Atlantic. SSHA variance at 35degrees in the western half of the basin increases by similar to63% over that in the east, but the associated change in inferred first-mode baroclinic Rossby wave energy is a substantially smaller increase of similar to26% (similar to34%) for the standard (surface intensified) mode. This is mainly associated with increases to vertical mode surface intensification and squared internal gravity wave speed in the west due to stronger stratification above the pycnocline. The wind-forced wave equation for SSHA has a dimensionless coefficient of Ekman pumping that is proportional to the ratio between SSHA variance and wave energy, implying similar geographic variation in efficiency of wind excitation of Rossby wave SSHA.