A sverdrup model of the depth-integrated flow for the world ocean allowing for island circulations

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Abstract
The annual mean depth-integrated steric height P and stream function ψ of the world ocean are calculated from a Sverdrup model with Hellerman and Rosenstein's (1983) annual mean wifids. The parameterization of friction is unspecified, but friction is assumed to be important only along western boundaries. A simple rule, based on Sverdrup interior flow and geostrophy of longshore flow along western boundary currents, is used to calculate P at the inshore edge of the western boundary current. The substantial predicted longshore gradients of P drive the model western boundary currents against friction, independent of frictional parameterization. One corollary is an “Island Rule”–an explicit expression for circulation around an island, in terms of wind stress, again independent of frictional parameterization. The circulations around Australasia, New Zealand and Malagasy are calculated as 16±4 Sv, 29±v, and 4±3 Sverdrups respectively. Inclusion of island effects result in more accurate flow estimates in the Southern Hemisphere than have previously been obtained from Sverdrup models. The calculated world field of P is compared with observed depth-integrated steric height, relative to various depths of no motion, obtained from the Levitus world data set; the tropics of all oceans and the Antarctic Circumpolar Current are quite well described, but in the model an unrealistic pair of zonal jets crosses the Atlantic just south of South Africa, and the model fails in the subpolar gyres of the Northwest Atlantic and Pacific. The observed difference in annual mean P from Western Australia to Indonesia suggests a Pacific-Indian Ocean throughflow of about 12 Sverdrups. Observed values of P near each of seven oceanic eastern boundaries lie close to a single, characteristic value for that boundary; the model predicts differences between these characteristic values quite well. This may, for example, explain Reid's (1961) observations of quite large density differences between the Atlantic and Pacific Oceans. The model calculations are repeated with the Indonesian passages closed. In the model, the Indian Ocean becomes very much “colder”; the predicted drop in P could be created by a uniform drop of temperature of 6°C in the top 500m over the entire South Indian Ocean, with smaller changes elsewhere. More generally, there may be important implications for world climate in previous geological eras, when the distribution of continents was different from today.