Technical Note: Volume Transport Equations in Combined Sverdrup-Stommel-Munk Dynamics without Level of no Motion

Abstract. The cornerstone theories of ocean dynamics proposed by Sverdrup (1947), Stommel (1948), and Munk (1950) are based on the assumption of level of no motion. Such an assumption is the same as the assumption of no meridional geostrophic transport. Ever since Sverdrup (1947) however, verification of the accuracy of the Sverdrup balance theory is based on the comparison of the Sverdrup meridional transport with the meridional transport calculated directly from the geostrophic currents based on hydrographic data. To overcome the mismatch between theory (no meridional geostrophic transport in Sverdrup transport) and verification (comparison of Sverdrup transport to meridional geostrophic transport), extended Sverdrup-Stommel-Munk transport equations are derived in this note with replacing the level of no motion by the ocean bathymetry and in consequence one forcing function (surface wind stress) in the classical transport equations (with level of no motion assumption) is replaced by five forcing functions: density, surface wind stress, bottom meridional current, bottom stresses due to vertical and horizontal viscosities. The first two forcing functions (density and surface wind stress) are more than an order of magnitude stronger than the other three forcing functions using the world ocean bathymetry, climatological annual mean hydrographic and surface wind stress data. The extended Sverdrup volume transport streamfunctions under wind forcing, density forcing, and combined wind and density forcing are presented.