Fig. 3.21 The time evolution of the normalized wind energy input through the geostrophic current (circles), surface waves (inverted triangles), and Ekman layer (squares) (Huang et al., 2006).

Changes in wind stress energy input Perhaps the most important point deserving serious attention is that wind stress energy input to surface geostrophic current varies greatly from year to year, and has been increasing over the past 50 years, as shown in Figure 3.20.

Similarly, wind energy input to surface waves and the Ekman layer has also increased noticeably over the past decades (Fig. 3.21). Variations in wind energy input to the oceans have originated from different sources. First, due to global warming, wind and other nonlinear dynamical processes may be more energetic. Second, the ozone hole which first appeared near the South Pole is capable of intensifying the southern polar vortex. Through wave-wave interactions in the atmosphere, the intenstification of the polar vortex propagates downward and manifests as the intensification of the south-westerly and enhances the surface west wind over the Southern Ocean (see, e.g., Yang et al., 2007).

As shown in these two figures, we can see, thanks to the availability of reliable measurements, including satellite data, that energy input to the oceans, through geostrophic currents, ageostrophic currents, and surface waves, has kept increasing steadily since the 1980s. Thus, it is natural that the oceanic general circulation should adjust in response to such changes in energy input.

Changes in tidal dissipation

Many factors regulate tidal dissipation, including the shape of the basin, bathymetry, and sea level. These aspects of boundary conditions change over a wide range of time scales.

-©— Energy input to surface current (Model) ■V— Energy input to surface waves -h— Energy input to Ekman layer

1950 1960 1970 1980 1990 2000

Global-scale changes in land-sea distribution due to continental drift

These changes have a millennial or longer time scale. Due to changes in the size and shape of the basins, tidal dissipation has varied greatly over the geological past; thus, the energy supporting diapycnal mixing may vary as well (Fig. 3.22). Note that this result was based on a numerical model with a flat bottom. It is well known that bottom topography plays a vitally important role in controlling the barotropic tidal flow and dissipation; however, reconstruction of the paleotopography may be very challenging. Thus, the results from a simple tidal model are quoted here to demonstrate the basic idea that tidal dissipation may have changed tremendously over the geological past.

If we go further back into the geological past, the change in the gravitational field of the Earth-Moon system and the rotation rate of the Earth may also have to be taken into consideration. Paleo records indicate that the Earth's rotation has slowed down over the past 900 million years; this should have affected the tidal flow and dissipation rate.

Owing to the movement of the mantle, continents have drifted greatly over the geological past. Accordingly, the shape of the world's oceans has also changed dramatically. It is a grand challenge to map out the position and bathymetry of the oceans and the associated tidal flows.


Fig. 3.22 Changes in the M2 tidal dissipation (thick line, in 1012 W), KE (dashed line, in 1017 J), and potential energy (thin line, in 1017 J), over the past 550 million years (based on data from Kagan and Sundermann, 1996).


Fig. 3.22 Changes in the M2 tidal dissipation (thick line, in 1012 W), KE (dashed line, in 1017 J), and potential energy (thin line, in 1017 J), over the past 550 million years (based on data from Kagan and Sundermann, 1996).

Global sea-level change

On time scales shorter than millennial, the mean sea level of the world's oceans can change due to the glacial-interglacial cycles. For example, during the Last Glacial Maximum (LGM), great changes took place, resulting in a tidal dissipation and thermohaline circulation that were substantially different, including the following:

• Sea level was more than 100 m lower than at present. Tidal dissipation in shallow seas was much reduced. As a result, tidal flow in the deep oceans was much faster. Hence, global tidal dissipation during the LGM was 50% higher than at present (Egbert et al., 2003).

• The meridional temperature difference in the atmosphere was larger, so the wind was much stronger; thus wind energy input into the ocean was much stronger.

Thus, it would be an excellent project to simulate the oceanic circulation and climate during the LGM with a new parameterization of diapycnal mixing which changes with climate.

Gravitational potential energy is one of the most important components in the energy balance of the oceanic general circulation. In order to make full use of the mass conservation rule, the definition of GPE can be conveniently rewritten in the mass coordinate, using pdv = dm, so that

Note that the value of GPE depends on the choice of reference level. For example, using the sea surface as a reference level will give rise to a negative value for GPE. Using the mean seafloor depth of the ocean, D = -3750 m, as the reference level, the total amount of GPE in the world's oceans is estimated as 2.1 x 1025 J (/ ~ 1.4 x 107J/m3).

The density of seawater varies only slightly. Therefore, a major part of GPE in the ocean is dynamically inert, so that only a small part of this energy associated with the density deviation from the mean value is dynamically active. Different ways of differentiating between the dynamically active and non-active components of GPE exist, such as the conceptions of stratified GPE (SGPE) and available potential energy (APE), which are discussed in the following sections.

3.7 Gravitational potential energy and available potential energy 3.7.1 Gravitational potential energy

The density of GPE is defined as

Because seawater is almost constant, mass conservation is replaced by volume conservation in the commonly used Boussinesq approximations. However, replacing mass conservation by volume conservation can induce an artificial source/sink of mass and GPE in the models. In order to avoid such problems, one should use a model based on mass conservation for studying the GPE balance.

Definition of stratified gravitational potential energy The basic idea of SGPE is to separate GPE into two parts: the part due to the basin mean density and the part due to the density anomaly. We define the global mean depth, density, and reference pressure as

For the world's oceans z = -2365 m, p = 1038.43 kg/m3, p = 2455 db. Accordingly, the integrand of GPE in Eqn. (3.136) can be separated into two parts pz = pz + p'z!, because the other terms, pz' and p'z, make no contribution to the global integral. Therefore, the total GPE can be separated into two parts are the GPE associated with the mean density and the SGPE associated with the stratification. While $0 is reference-level dependent, is not and its density is estimated as x ' = /V ~ -1.0 x 105//m3 for the world's oceans. x' is negative because p' and z' are negatively correlated. Apparently, SGPE reflects the energy associated with the vertical stratification; however, most of such energy cannot be converted into KE, and thus it is not an effectively usable energy source for driving the oceanic circulation. By definition, if water density is homogeneous, SGPE should be zero.

To examine the contributions to SGPE from pressure, temperature, and salinity, we introduce the following decomposition p'z' = [(p - am) + (&m0 - äm) + (öm - p) + (am - ^mo)l (Z - Z) (3.141)

where p is the in situ density; am = am (T, S,p,pf) is the potential density, using pr = 2455 db as the reference pressure; and am0 = am (T, S,p,pf) ; S = 34.718 is the mean salinity; am = jjjV amdv/V = 1038.70kg/m3, so the difference between p and am is small.


From the definition of z, the global integration of the third term in Eqn. (3.141) vanishes, i.e., //fv (am - P)(z - z)dv = 0. Thus, SGPE can be separated into three components

Now let us look at these terms more closely. The first term, $>p = .f.f.iv (P - am) (z - Z^)dv, is due to the density anomaly associated with pressure difference. Since the compressibility of seawater is roughly constant, p - am is a nearly linear function of z, with a zero value at the reference level, (p - am)(z - z) < 0 for the whole water column. Because the compressibility of seawater varies with change in salinity and temperature only very slightly, this term is roughly proportional to the square of the ocean depth at each location (Fig. 3.23).

The second term in Eqn. (3.142), $T = fffv (am0 - am) (z - z)dv, reflects the density difference due to temperature in the ocean. In the subtropics, warm water in the upper ocean gives rise to a large difference of am0 - am < 0. In the Atlantic sector, the density anomaly is positive only for the small part where the Antarctic Bottom Water (AABW) dominates (see Fig. 3.24a). Beginning with the large negative value in the warm water pool, the contribution due to temperature remains negative everywhere in the Pacific sector, except for small areas near the Antarctic and in the Arctic Ocean (see Fig. 3.24b).

Stratified GPE due to pressure (106J/m2)

Stratified GPE due to pressure (106J/m2)

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Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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