The Ekman and windinduced geostrophic flows

We show first that the wind does indeed induce a geo-strophic flow that has the same sense as the wind itself. The mean winds are to the east in midlatitudes and to the west in the tropics and, as we showed in the section in chapter 3 on Ekman layers, there is a flow in the upper Figure 4.2. Production of gyres by winds. The winds blowing as shown induce a converging Ekman flow, causing the sea level to increase in the center, thus giving rise to a pressure gradient. This gradient in turn...

Ocean structure and circulation

The aspect of the ocean that perhaps most affects the climate is the temperature distribution at the surface the MfE WE 180 1 W 60W 0- Figure 2.2. The annual average temperature at the ocean surface, in degrees centigrade. Adapted from World Ocean Atlas, 2009 of the National Oceanic and Atmospheric Administration (http www.nodc .noaa.gov OC5 WOA09 pr_woa09.html). MfE WE 180 1 W 60W 0- Figure 2.2. The annual average temperature at the ocean surface, in degrees centigrade. Adapted from World...

Ocean eddies

We are all familiar with the fact that the weather differs from the climate, the difference arising because the atmospheric flow is unsteady, and we talk more about this in chapter 6. The same applies to the ocean, only more so the large-scale currents in the ocean are almost all unstable, rather like a river flowing over rapids, and tend to break up into smaller mesoscale eddies, as illustrated in the lower panel of figure 2.6. The resulting eddies are the oceanic analogue of atmospheric...

Appendix A Mathematics Of The Twobox Model

Here we give a mathematical description of the two-box model of the ocean, illustrated in figure 7.9. The evolution equations of the two boxes are Cm dTm F miTm m (Tm Td), (7.2a) Figure 7.9 A simple two-box model of the ocean, with a mixed layer at a temperature Tm and a deep ocean layer at a temperature Td, and exchanges of heat between the components as shown. Figure 7.9 A simple two-box model of the ocean, with a mixed layer at a temperature Tm and a deep ocean layer at a temperature Td, and...

HYDRoSTATic BALANcE

Let us now consider what the balance of forces is in the vertical direction. A moment's thought indicates that there must be a pressure gradient in the vertical direction, because without one there would be nothing to hold up the fluid. A piece of fluid, be it a piece of air or a piece of seawater, is not weightless, so the force of gravity acts on it, pulling it down toward Earth. If the fluid parcel is stationary, then there must be a force in the opposite direction that balances gravity, and...

Greenhouse effect

Earth is covered with a blanket of gas made mainly of nitrogen, oxygen, carbon dioxide, and water vapor. This blanket is essential to life on Earth, for (at least) two reasons 1. We breathe the air, taking in the oxygen and breathing out carbon dioxide. Similarly, plants use sunlight together with the carbon dioxide in the atmosphere to photosynthesize and create organic compounds. 2. The atmosphere absorbs the infrared or longwave radiation emitted by Earth's surface and re-emits it back to...

Global Warming iN Context The Past Millennium

When discussing global warming, a fair question to ask is, How does the temperature increase of the past century compare with other periods in the past It is a difficult question to answer precisely because we only have direct measurements of surface temperature for the past 140 years or so, although a few individual records go back further there is a record of measured temperatures in central England from 1659, for example. However, the use of various proxies enables the construction of the...

The centrifugal force

In this section, we derive an expression for the centrifugal force on a body moving in a circle of radius r with an angular velocity Q, as illustrated in figure 3.5. Let us first consider what forces are involved in a body that is moving in a circle with a uniform speed. Newton's first law of motion says that if a body is left to its own devices it will either remain stationary or move in a straight line with a constant speed. If a body is undergoing uniform circular motion (for example, a...

Implications for global warming

Earlier we noted that one possible cause of the warming over the past century is natural variability, with one candidate mechanism being a variation in the ocean that releases heat to the atmosphere, thus causing atmospheric warming. This is a very plausible conjecture because the ocean certainly has the potential to vary on the timescale of decades to centuries however, the empirical evidence is against it. If the ocean were to have given up its heat to the atmosphere, then it would have...

The lag in the seasons

The observant reader noted in figure 5.1 that not only is the seasonal cycle more muted in San Francisco, but also that the maximum temperatures occur later in the season, in September. This again is an effect of the large heat capacity of the system, as a simple argument shows. Suppose that a system is heated externally (e.g., by the sun) and is cooled by the effects of longwave radiation and that the cooling is proportional to the temperature itself. If the system has a very small heat...

Western iNTENSiFicATioN

We have now explained the underlying reason for gyres, but we have not explained one of their most important and indeed obvious aspects the gyres are not symmetric in the east-west direction. Thus far, our explanation would lead to gyres that look like those in the left panel of figure 4.3, whereas in fact the gyres look more like those in the right-hand panel, with intense western boundary currents, of which the Gulf Stream in the western North Atlantic is the most famous example to Americans...

PoSSiBLE cAuSES of GLoBal WarmiNG The likely culprit

The atmosphere contains greenhouse gases that absorb and re-emit longwave (infrared) radiation, thus warming the surface. If the greenhouse gas concentration increases, we can therefore expect temperatures to rise. Thus, a reasonable hypothesis is that the increase in anthropogenic greenhouse gases, and in particular CO2, over the past several decades is responsible for the increase in temperature. In chapter 1 we constructed a very simple mathematical model of this process we now present a...

THE MoDERATiNG iNFLuENcE of the ocean

Perhaps the most obvious effect that the ocean has on climate is its moderating effect on extremes of temperature, both diurnally (i.e., the day-night contrast) and annually (the seasonal cycle). We focus on the effects on the annual cycle because these tend to be on a larger scale and more befitting a book with climate in the title, but much the same principles and effects apply to the diurnal cycle. First we take a look at the observations to confirm that there is a moderating influence from...

Differential rotation and Earths sphericity

Finally, let us consider the effect of Earth's sphericity on the Coriolis force. The rotation axis of Earth is a line between the North Pole and the South Pole, and the Co-riolis force always acts in a direction perpendicular to this line. We are primarily interested in the horizontal deflection of fluid parcels by the Coriolis force because in the vertical direction, gravitational effects dominate and the Coriolis force is relatively small. The horizontal deflection is caused mainly by the...

Westward drift

In this section, we give a slightly different explication of why the boundary current is in the west. It is not really a different explanation because the cause is still differential rotation, but here we think about it quite differently. We'll see that the effect of differential rotation is to make patterns propagate to the west, and hence the response to the wind's forcing piles us in the west and produces a boundary current there. We noted already that the component of Earth's rotation in...

The Planet Earth

Earth is a planet with a radius of about 6,000 km, moving around the sun once a year in an orbit that is almost circular, although not precisely so. Its farthest distance from the sun, or aphelion, is about 152 million km, and its closest distance, perihelion, is about 147 million km. This ellipticity, or eccentricity, is small, and for most of the rest of the book we will ignore it. (The eccentricity is not in fact constant and varies on timescales of about 100,000 years because of the...

Magnitude of the Coriolis force

There is a simple way we can calculate the Coriolis force on a body moving zonally (i.e., in the east-west direction) if we already know the form of the centrifugal force. For simplicity, we first suppose that Earth is a flat disk, with the axis of rotation perpendicular to the disk and passing through the disk's center, which is then analogous to the North Pole. Gravity points down into the disk. (We consider the effects of sphericity in the next section until then, Earth is flat.) Let Earth's...

Centrifugal Force

Suppose that you are riding in a train that starts to go around a bend rather quickly. You feel like you are being thrust outward toward the side of the car, and if you are really going quickly around a tight curve, you might have to hang onto something to stay put. The outward force that you are feeling is commonly known as centrifugal force. Strictly speaking, it is not a force at all (we'll explain that cryptic comment later), but it certainly feels like one. What is going on One of the most...

The buoyancy or Archimedean force

The force due to buoyancy is one of the most familiar forces occurring in a fluid and, rather famously, was known to Archimedes. It is the force that, among other things, allows objects to flow in water. The Archimedes principle is often stated as Any object, partially or wholly immersed in a fluid, experiences an upward force equal to the weight of the fluid displaced by the object. Let's see why this is so. Consider a container of still water and focus attention on a particular piece of water...

What are the important greenhouse gases

The most important greenhouse gases in Earth's atmosphere are water vapor and carbon dioxide, followed by ozone, nitrous oxide, methane, and various other gases (see table 1.1). Water vapor (and clouds) and carbon dioxide have the dominant effect, although their respective levels are maintained in different ways. The level of C02 is almost constant throughout the atmosphere, and year by year its level is maintained by a balance between emissions (e.g., respiration by animals and bacteria) and...

The general damping of climate variability by the ocean

N> t only does the ocean provide a moderating influence on the march of the seasons, but it also can provide a moderating influence on the variability of climate on other timescales too. We talk more about the mechanisms that give rise to climate variability in the next chapter, but for now let us just suppose that the climate system excluding the ocean is able to vary on multiple timescales, from days to years. Then, just as the ocean is able to damp the seasonal variability, the ocean damps...

The mechanism of El

The mean state of the atmosphere and the ocean Before discussing what processes conspire to produce El Ni o events, let us discuss what the mean state of the atmosphere and ocean are, beginning with the atmosphere. The trade winds throughout the equatorial region blow predominantly from higher latitudes toward the equator, and from the east to the west. The low-level convergence at the equator forces the air to rise and then, several kilometers above the surface, move poleward, sinking in the...

THE CORiOLiS FORCE

Another apparent force is caused by Earth's rotation, one that only arises when bodies are in motion relative to the rotating Earth, and this force is known as the Coriolis force after the French engineer and scientist Gaspard-Gustave Coriolis (1792-1843). It turns out to be much more important than the centrifugal force for currents and winds, although its effects are rather subtle. The sphericity of Earth is not important in the coriolis force itself, and until we get to the section on...

The overturning circulation and the vertical structure

The meridional overturning circulation (MOC) of the ocean is the name commonly given to the circulation in the meridional (i.e., north-south and up-down in water depth) plane. Horizontal variations in this circulation can be important, but let us put them aside for now. This circulation comes about as a consequence of various factors the temperature gradient between equator and pole, the temperature difference between high northern latitudes and high southern latitudes, the winds, especially...

Loss Of Sea iCE

Sea ice is formed by the freezing of seawater and so is to be found at high latitudes in both the Northern and Southern hemispheres, especially in their respective winters and springs. Sea ice is important to the climate system because it has a higher albedo than seawater (and therefore reflects back more solar radiation to space), because it affects the way the atmosphere and ocean exchange heat and water vapor, and because when sea ice forms, salt is extruded into the ocean, and when it...

A simple radiation model

Let us put aside the spatial variation of solar radiation for a while and try to obtain an estimate of the average surface temperature on Earth, given the average solar radiation coming in at the top of the atmosphere. Solar radiation causes Earth's surface to warm and emit its own radiation back to space, and the balance between incoming and outgoing radiation determines the average temperature of Earth's surface and of the atmosphere. To calculate the temperature, we need to know a few pieces...

The horizontal structure and the ocean currents

A schematic of the main horizontal ocean currents at the ocean surface is shown in figure 2.3. In most regions of the world, these currents extend a few hundred meters into the ocean, with the exception of the equatorial region. Here there is a shallow westward-flowing surface current and a more substantial eastward flow beneath (as well as narrow countercurrents on either side of the westward flow, not shown in the schematic). At first glance, the circulation seems complicated, especially as...

Torques and interior flow

If the wind stress acting on the ocean varies with latitude as we see that it does in figure 4.3 then the wind provides a torque that tends to spin the ocean. In a steady state, not only do the forces on the ocean have to balance but so do the torques otherwise the ocean would spin faster and faster. The torques on the ocean are provided by the wind, by friction, and by the Coriolis force (the pressure gradient does not provide a torque).2 Integrated over the entire ocean basin, the wind torque...

A simple mathematical model of the greenhouse effect

Let us now construct a simple mathematical model illustrating the greenhouse effect. our purpose in doing so is to see somewhat quantitatively, if approximately, whether the atmosphere might warm the surface up to the observed temperature. Let us make the following assumptions 1. The surface and the atmosphere are each characterized by a single temperature, Ts and Ta, respectively. 2. The atmosphere is completely transparent to solar radiation. 3. Earth's surface is a blackbody. 4. The...