or, dividing through by N2, Eq. 9-6, we find that the slope of isopycnals—interior density surfaces—must be related to the slope of the free surface by:

I isopycnal slope |

I free surface slope | .

Using our estimate of N2 in Section 9.1.5 and rearranging, we find that g/N2H « 400 if we assume that H = 1 km. Thus we see that for every meter the free surface tilts up, density surfaces must tilt down by around 400 m if deep pressure gradients, and hence deep geostrophic flows, are to be cancelled out. But this is just what we observe in, for example, Fig. 9.5. In those regions where the sea surface is high—over the subtropical gyres (see Fig. 9.19)—density surfaces bow down into the interior (see Fig. 9.8). In the subpolar gyre (where the sea surface is depressed) we observe density surfaces bowing up toward the surface. It is these horizontal density gradients interior to the ocean that ''buffer out'' horizontal gradients in pressure associated with the tilt of the free surface; in the time-mean, the second term in Eq. 9-12 does indeed tend to cancel out the first. This is illustrated schematically in Fig. 9.20.

9.3.3. Steric effects

A major contribution to the spatial variations in the height of the ocean surface shown in Fig. 9.19 is simply the expansion (contraction) of water columns that are warm (cold) relative to their surroundings. Note that the sea surface is high over the subtropical gyres, which are warm, and low over the subpolar gyres and around Antarctica, which are relatively cold. Similarly, salty columns of water are shorter than fresh columns, all else being equal. This expansion/contraction of water columns due to T and S anomalies is known as the steric effect. We can estimate its magnitude from Eq. 9-13 as follows:

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