## Problems

1. It is observed that water sinks in to the deep ocean in polar regions of the Atlantic basin at a rate of 15 Sv.

(a) How long would it take to fill up the Atlantic basin?

(b) Supposing that the local sinking is balanced by large-scale upwelling, estimate the strength of this upwelling. Express your answer in m y-1.

(c) Assuming that pv = f dw/dz, infer the sense and deduce the magnitude of the meridional currents in the interior of the abyssal ocean where columns of fluid are being stretched.

(d) Estimate the strength of the western boundary current.

2. Review Section 11.3.3, but now suppose that boundary currents flow northwards in Fig. 11.20. By considering the role of boundary current friction in inducing Taylor columns to stretch/compress (Eq. 11-10), deduce that northward flowing eastern (western) boundary currents are disallowed (allowed).

3. Consider the laboratory experiment GFD XV: source sink flow in a rotating basin. Use the Taylor-Proudman theorem and that eastern boundary currents are disallowed, to sketch the pattern of flow taking fluid from source to sink for the scenarios given

FIGURE 11.33. Possible placement of the source and sink in GFD LabXV: source sink flow in a rotating basin. Note that Fig. 11.22 corresponds to the case at the bottom of the column on the left.

in Fig. 11.33. Note that one of the solutions is given in Fig. 11.22!

4. From Fig. 11.6 one sees that evaporation exceeds precipitation by order 1 my-1 in the subtropics (± 30°), but the reverse is true at higher latitudes (± 60°).

(a) Estimate the meridional freshwater transport of the ocean required to maintain hydrological balance and compare with Fig. 11.32.

(b) Latent heat is taken from the ocean to evaporate water, which subsequently falls as rain at

(predominantly) higher latitudes, as sketched in Fig. 11.5. Given that the latent heat of evaporation of water is 2.25 x 106 J kg-1, estimate the implied meridional flux of energy in the atmosphere and compare with Fig. 8.13. Comment.

5. In the present climate the volume of freshwater trapped in ice sheets over land is ~33 x 106 km3. If all this ice melted and ran into the ocean, by making use of the data in Table 9.1, estimate by how much the sea level would rise. What would happen to the sea level if all the sea-ice melted?