On the Effect of Heat and Fresh Water Fluxes Across the Ocean Surface, in Volume-Conserving and Mass-Conserving Models

Abstract

A simple two-layer model is used to study changes in sea level forced by fresh water and heat fluxes across the ocean surface, including the dynamical effects related to induced pressure gradients. These solutions (η _E & η _Q ) are compared with the expected expansion of the water column (η _S & η _T ) related to the salinity and temperature changes produced by the local fresh water and heat fluxes which are restricted to a surface layer. Deeper salinity and temperature variations produced by the induced pressure gradients, are excluded from the definition of η _S and η _T .

Two conditions must be met to attribute sea level variations to an expansion or contraction of the water column. First, the sea level produced by the surface fluxes, η _E & η _Q , must be close to η _S & η _T . Second, this result must be obtained with a mass-conserving model that allows for the thermohaline expansion of seawater, but not with the usual volume-conserving model.

The information on the horizontal wavenumber and frequency of the forcing is contained in a single variable with two very different normalizations: κ ₀ & κ ₁, where κ ₀ = 1 and κ ₁ = 1 represent the dispersion relation for barotropic and baroclinic Poincaré waves respectively.

For very long horizontal scales, κ ₀ ≪ 1, the total response to heat forcing η _Q coincides with η _T . This effect is not predicted by a volume-conserving model. On the other hand, the effect of precipitation and evaporation is to raise and lower the surface by adding or subtracting water, its impact on water density is much less important, i.e. η _E ≫ η _S and can be safely modelled with a volume-conserving model. At long scales, κ ₀ ≈ O (1), the solution is related to the forcing of the barotropic mode. Mass-conserving equations are still crucial to obtain η _Q correctly, but are not necessary for η _E . A single (thermohaline active) layer model with a rigid bottom, behaves like the two-layer model at these scales.

Finally, at short scales, κ ₁ ≈ O(1), the response is controlled by the forcing of the baroclinic mode and mass-conserving equations are not needed. If the top layer is relatively shallow, the behavior at short and intermediate (κ ₁ ∼ κ ⁻¹₀ ≪ 1) scales is similar to that of a reduced gravity model with a single (thermohaline active) layer. In this case, sea level equals the dynamic height relative to the lower layer. This effect is totally unrelated to the expansion or contraction of the water column.