Climate Dynamics

The Atmospheric Absorption Spectrum

Absorption Spectra Goody 1989

A property of the blackbody radiation curve is that the wavelength of maximum energy emission, Xm, satisfies This is known as Wien's displacement law. Since the solar emission temperature is about 6000 K, the maximum of the solar spectrum is (see Fig. 2.2) at about 0.6 m (in the visible spectrum), and we have determined Te 255 K for the Earth, it follows that the peak of the terrestrial spectrum is at XEmarth 0.6 m x 6000 - 14 Mm. 255 Thus the Earth's radiation to space is primarily in the...

Moist Convection

Moist Convection

We have seen that the atmosphere in most places and at most times is stable to dry convection. Nevertheless, convection is common in most locations over the globe (more so in some locations than in others, as we will discuss in Section 4.6.2). There is FIGURE 4.17. (Top) A satellite image showing dense haze associated with pollution over eastern China. The view looks eastward across the Yellow Sea toward Korea. Provided by the SeaWiFS Project, NASA Goddard Space Flight Center. (Bottom)...

Radiative Forcing And Temperature

Global Radiation Diffuse

The latitudinal distribution of incoming solar radiation at the top of the atmosphere in the annual mean and at solstice is shown in Fig. 5.2. Its distribution is a consequence of the spherical geometry of the Earth and the tilt of the spin axis, depicted in Fig. 5.3. If the Earth's axis did not tilt with respect to the orbital plane, the average incident flux would maximize at a value of Smax So n 435Wm-2 at the equator, and fall monotonically to zero at the poles. Because of the tilt,...

Paleoclimate

Glacial Maximum Pennsylvania

Here we briefly review something of what is known about the evolution of climate over Earth history. Fig. 12.12 lists standard terminology for key periods of geologic time. Study of paleoclimate is an extremely exciting area of research, a fascinating detective story in which scientists study evidence of past climates recorded in ocean and lake sediments, glaciers and icesheets, and continental deposits. Proxies of past climates are myriad, and to the uninitiated at least, can be bizarre...

Radiativeconvective Equilibrium

As we saw in Section 3.1.2, the thermal structure expected on the basis of radiative forcing alone has a temperature discontinuity at the ground, as illustrated in Fig. 3.4 the radiative equilibrium temperature of the ground is considerably warmer than that of the air above. This profile is unstable and convection will occur. Convective motions will transport heat upward from the surface when the air parcels mix with the environment (as they will), they increase the environmental temperature...

Problems

Show that the buoyancy frequency, Eq. 4-22, may be written in terms of the environmental temperature profile thus where rd is the dry adiabatic lapse rate. 2. From the temperature (T) profile shown in Fig. 4.9 (a) Estimate the tropospheric lapse rate and compare to the dry adiabatic lapse rate. (b) Estimate the pressure scale height RT0 g, where To is the mean temperature over the 700 mbar to 300 mbar layer. (c) Estimate the period of buoyancy oscillations in mid-troposphere. 3. Consider the...

Mechanistic View Of The Circulation

To what extent can we explain the main features of the observed general circulation on the basis of the fluid dynamics of a simple representation of the atmosphere driven by latitudinal gradients in solar forcing The emphasis here is on simple. In reality, the Earth's surface is very inhomogeneous there are large mountain ranges that disturb the flow and large contrasts (e.g., in temperature and in surface roughness) between oceans and continents. In the interests of simplicity, however, we...

The Observed Mean Circulation

The global pattern of mean flow at the surface of the ocean is plotted in Fig. 9.13, where the names of the major current systems are also given. The colors separate the circulation patterns into tropical (pink), subtropical (yellow), and subpolar (blue) regimes (inspired by the dynamical discussion to be developed in Chapter 10). Because the detailed patterns are difficult to discern on this global map, regional circulations in the Pacific, Atlantic, and Indian Oceans are also shown in Figs....

The Observed Thermohaline Circulation

The time-mean abyssal flow in the ocean is so weak that it cannot be measured directly. However abyssal circulation, and the convective processes forcing it, leaves its signature in the distribution of water properties, from which much can be inferred. 11.2.1. Inferences from interior tracer distributions Water masses modified by deep convection are tagged with T and S values characteristic of their formation region, together with other tracers, such as tritium from the atomic weapon tests of...

Dynamical Models Of The Thermohaline Circulation

Vistas Cuerpos Solidos

Abyssal circulation schematic deduced from Taylor-Proudman on the Because of the paucity of direct observations of abyssal flow, theory has been an invaluable guide in deducing likely circulation patterns. The starting point for a theoretical deduction are two important inferences from the observations discussed above 1. Dense water is formed at the surface in small, highly localized regions of the ocean in polar seas. Thus the abyssal circulation seems to be induced by local sources,...

Observations Of Abyssal Ocean Circulation

It is very hard to test whether the circulation schematic, Fig. 11.16, has parallels in the ocean because the predicted mean currents are so very weak and the variability of the ocean so strong. However, one of the key predictions of Stommel's abyssal theory was that there ought to be deep western FIGURE 11.22. Three photographs charting the evolution of dye from source (white circle) to sink (black circle) using the apparatus shown in Fig. 11.21. The shallow end of the tank is marked with the...

A5 Figures And Access To Data Over The

The vast majority of the data and figures presented in this book were accessed and plotted using the Climate Data Library of the International Research Institute of the Lamont-Doherty Earth Observatory of Columbia University. The library contains numerous datasets from a variety of Earth science disciplines and climate-related topics, which are accessible free over the web see http iridl.ldeo.columbia.edu . Web-based tools permit access to data sets, analysis software for manipulation of the...

Convection In The Atmosphere

Cumulus Clouds Level Atmosphere

We have seen that the atmosphere is normally stable in the absence of condensation. Hence most convection in the atmosphere is moist convection, accompanied by saturation and hence cloud formation. Downwelling air parcels do not become saturated because descending air FIGURE 4.20. Schematic of convective clouds Cu cumulus Cb cumulonimbus. The condensation level is the level above which q q . Cb clouds have a characteristic ''anvil,'' where the cloud top spreads and is sheared out by strong...

Physical Properties Of

Some important numbers for Earth's atmosphere are given in Table 1.3. Global mean surface pressure is 1.013 x 105Pa 1013 h Pa. (The hecto Pascal is now the official unit of atmospheric pressure 1 h Pa 102 Pa , although the terminology millibar 1 mbar 1 h Pa is still in common use and will also be used here.) The global mean density of air at the surface is 1.235 kgm-3. At this average density we require a column of air of about 7-8 km high to exert pressure equivalent to 1 atmosphere....

A3 Use Of Foraminifera Shells In Paleo Climate

A key proxy record of climate is 518O, the ratio of 18O to 16O in the shells of surface (planktonic) and bottom (benthic) dwelling foraminifera which are made of calcium carbonate, CaCO3. The 518O in the shell, measured and reported as where (18O 16O)smpl is the ratio of 18O to 16O in the sample and (18O 16O)sd is the ratio in a standard reference, is controlled by the 518O value of the water and the temperature at which the shell formed. It turns out that 18O is increasingly enriched in CaCO3...

Vertical Distribution Of Temperature And Greenhouse Gases

Label Atmospheric Layer

Temperature varies greatly both vertically and horizontally (as well as temporally) throughout the atmosphere. However, despite horizontal variations, the vertical structure of temperature is qualitatively similar everywhere, and so it is meaningful to think of (and to attempt to explain) a typical temperature profile. (We look at horizontal variations in Chapter 5.) A typical temperature profile (characteristic of 40 N in December) up to about 100 km is shown in Fig. 3.1. The profile is not...

Physical Characteristics Of The Ocean

The ocean covers about 71 of the Earth's surface and has an average total depth of 3.7 km the distribution of land and sea and the bathymetry of the ocean basins is plotted in Fig. 9.1. A north-south section along the Greenwich meridian through Fig. 9.1 is shown in Fig. 1.2. We see that the ocean basins are highly complex and the bottom topography much more jagged than that of the land surface. See also the bathymetry shown in the hydrographic section of Fig. 9.9. This is because, as we shall...

The thermohaline circulation of the ocean

Abyssal Circulation

Air-sea fluxes and surface property distributions 11.1.1. Heat, freshwater, and buoyancy fluxes 11.1.2. Interpretation of surface temperature distributions 11.1.3. Sites of deep convection 11.2. The observed thermohaline circulation 11.2.1. Inferences from interior tracer distributions 11.2.2. Time scales and intensity of thermohaline circulation 11.3. Dynamical models of the thermohaline circulation 11.3.1. Abyssal circulation schematic deduced from Taylor-Proudman on the sphere 11.3.2....

The Ocean Heat Budget And Transport

Heat Transport Atlantic Northward

We now turn to the role of the ocean circulation in meridional heat transport. To maintain an approximately steady climate, the ocean and atmosphere must move excess heat from the tropics to the polar regions. We saw back in Fig. 8.13 that the atmosphere SO FIGURE 11.24. Observations of CFCs at a depth of 2 km (contoured). Superimposed in red is a snap-shot for 1983 of the CFC distribution at a depth of 2 km in the North Atlantic, as simulated by a numerical model of ocean circulation and...

Energetics Of The Thermal Wind Equation

The immediate source of kinetic energy for the eddying circulation observed in our baroclinic instability experiment and in the middle-latitude atmosphere, is the potential energy of the fluid. In the spirit of the energetic discussion of convection developed in Section 4.2.3, we now compute the potential energy available for conversion to motion. However, rather than, as there, considering the energy of isolated fluid parcels, here we focus on the potential energy of the whole fluid. It will...

Geostrophic And Hydrostatic Balance

On the large-scale, water obeys the same fluid dynamics as air so we have already derived the equations we will need Eq. 6-44 applies just as well to the ocean as to the atmosphere. One simplification we can make in application of these equations to the ocean is to recognize that the density varies rather little in the ocean (by only a few see Fig. 9.2), so we can rewrite the horizontal momentum equations Eq. 6-44a,b thus (using our local Cartesian coordinate system see Fig. 6.19) without...

Surface Wind Stress Nm2

Annual mean wind stress on the ocean. The green shading and contours represent the magnitude of the stress. Stresses reach values of 0.1 to 0.2 Nm-2 under the middle-latitude westerlies, and are particularly strong in the southern hemisphere. The arrow is a vector of length 0.1 Nm-2. Note that the stress vectors circulate around the high and low pressure centers shown in Fig. 7.27, as one would expect if the surface wind, on which the stress depends, has a strong geostrophic...

The Taylorproudman Theorem

A remarkable property of geostrophic motion is that if the fluid is homogeneous (p uniform) then, as we shall see, the geostrophic flow is two dimensional and does not vary in the direction of the rotation vector, Q. Known as the Taylor-Proudman theorem, it is responsible for the glorious patterns observed in our dye shirring experiment, GFD Lab 0, shown again in Fig. 7.7. We discuss the theorem here and make much subsequent use of it, particularly in Chapters 10 and 11, to discuss the...

The Thermal Wind Equation

Taylor Proudman Ocean

We saw in Section 5.2 that isobaric surfaces slope down from equator to pole. Moreover, these slopes increase with height, as can be seen, for example, in Fig. 5.13 and the schematic diagram, Fig. 5.14. Thus according to the geostrophic relation, Eq. 7-8, the geostrophic flow will increase with height, as indeed is observed in Fig. 5.20. According to T-P, however, dug dz 0. What's going on The Taylor-Proudman theorem pertains to a slow, steady, frictionless, barotropic fluid, in which p p(p)....

The ocean and its circulation

Physical characteristics of the ocean 9.1.3. Properties of seawater equation of state 9.1.4. Temperature, salinity, and temperature structure 9.1.5. The mixed layer and thermocline 9.2. The observed mean circulation 9.3. Inferences from geostrophic and hydrostatic balance 9.3.1. Ocean surface structure and geostrophic flow 9.3.2. Geostrophic flow at depth We now begin our discussion of the circulation of the ocean. In this introductory chapter we describe the physical characteristics of...

The winddriven circulation

The wind stress and Ekman layers 10.1.1. Balance of forces and transport in the Ekman layer 10.1.2. Ekman pumping and suction and GFD Lab XII 10.1.3. Ekman pumping and suction induced by large-scale wind patterns 10.2. Response of the interior ocean to Ekman pumping 10.2.2. Wind-driven gyres and western boundary currents 10.2.3. Taylor-Proudman on the sphere 10.2.4. GFD Lab XIII Wind-driven ocean gyres 10.3. The depth-integrated circulation Sverdrup theory 10.3.1. Rationalization of...

Thermodynamic Equation

The equation governing the evolution of temperature can be derived from the first law of thermodynamics applied to a moving parcel of fluid. Dividing Eq. 4-12 by St and letting St > 0 we find DQ Dt is known as the diabatic heating rate per unit mass. In the atmosphere, this is mostly due to latent heating and cooling (from condensation and evaporation of H2O) and radiative heating and cooling (due to absorption and emission of radiation). If the heating rate is zero then DT Dt P- Dp Dt, and,...

Understanding The Observed Circulation

Angular Momentum Earths Circulation

The simplest observed global characteristic of the atmosphere is that the tropics are much warmer than the poles. As discussed in Chapter 5, this is a straightforward consequence of the geometry of the Earth the annually averaged incoming solar radiation per unit area of the Earth's surface is much greater at the equator than at the poles, a difference that is compounded by the fact that the polar regions are covered in ice and snow and therefore reflect much of the incoming radiation back to...

The Nature Of Convection

Convection in a shallow fluid When a fluid such as water is heated from below (or cooled from above), it develops overturning motions. It may seem obvious that this must occur, because the tendency of the heating (or cooling) is to make the fluid top-heavy.1 Consider the shallow, horizontally infinite fluid shown in Fig. 4.2. Let the heating be applied uniformly at the base then we may expect the fluid to have a horizontally uniform temperature, so T T(z) only. This will be top-heavy...

Equation Of Motion For A Nonrotating Fluid

The state of the atmosphere or ocean at any time is defined by five key variables (six if we include specific humidity in the atmosphere, or salinity in the ocean). Note that by using the equation of state, Eq. 1-1, we can infer p from p and T. To tie these variables down we need five independent equations. They are 1. the laws of motion applied to a fluid parcel, yielding three independent (x - g-Sx, y --g-Sy, z -g-Sz) (x + g-Sx, y -g-Sy, z --g-Sz) FIGURE 6.2. An elementary fluid parcel,...

Pref dX f dy f

The Ekman pumping velocity defined in Eq. 10-8 depends on the curl of (Twind f). Note, however, that typically Twind varies much more than f, and so the pattern of wEk is largely set by variations in Twind. We can estimate the magnitude of wEk as follows. Figure 10.2 shows that Twind changes from +0.1Nm-2 to -0.1Nm-2 over 20 of latitude, or 2000 km. Thus Eq. 10-8 suggests i in i inn im * v'vk v.-1 mivj h 'w ni li ii mi -hi h< ihi'i i < 11 FIGURE 10.11. The global...

The meridional structure of the atmosphere

Radiative forcing and temperature 5.1.3. The energy balance of the atmosphere 5.1.4. Meridional structure of temperature 5.2. Pressure and geopotential height In previous chapters we considered those processes that play a role in setting the vertical distribution of atmospheric properties. Here we discuss how these properties vary horizontally, on the global scale. We shall see that geometrical effects play a major role in setting the observed horizontal distribution. The spherical Earth...

Equations Of Motion For A Rotating Fluid

Fluid Watchers

Equation 6-6 is an accurate representation of Newton's laws applied to a fluid observed from a fixed, inertial, frame of reference. However, we live on a rotating planet and observe winds and currents in its rotating frame. For example the winds shown in Fig. 5.20 are not the winds that would be observed by someone looking back at the Earth, as in Fig. 1. Rather, they are the winds measured by observers on the planet rotating with it. In most applications it is easier and more desirable to work...

Ocean Eddies

Figures 9.14 to 9.16 show currents averaged over many (about 20) years of observations. However, just as in the atmosphere (in fact, even more so) the picture we have described of the general circulation of the ocean, while appropriate to the time-averaged flow, is inadequate for describing the instantaneous flow. There are large variations of currents and of surface height that, instantaneously, can mask the time-averaged picture. The altimetric and drifter data can be analyzed to yield...

Balanced flow

The geostrophic wind in pressure coordinates 7.1.2. Highs and lows synoptic charts 7.1.3. Balanced flow in the radial-inflow experiment 7.2. The Taylor-Proudman theorem 7.2.1. GFD Lab VII Taylor columns 7.3.1. GFD Lab VIII The thermal wind relation 7.3.2. The thermal wind equation and the Taylor-Proudman theorem 7.3.3. GFD Lab IX Cylinder ''collapse'' under gravity and rotation 7.3.4. Mutual adjustment of velocity and pressure 7.3.5. Thermal wind in pressure coordinates 7.4....

The general circulation of the atmosphere

Understanding the observed circulation 8.2. A mechanistic view of the circulation 8.2.1. The tropical Hadley circulation 8.2.2. The extra tropical circulation and GFD Lab XI Baroclinic instability 8.3. Energetics of the thermal wind equation 8.3.1. Potential energy for a fluid system 8.3.2. Available potential energy 8.3.3. Release of available potential energy in baroclinic instability 8.3.4. Energetics in a compressible atmosphere 8.4. Large-scale atmospheric energy and momentum budget...

Effects Of Stratification And Topography

Our analysis of the wind-driven circulation in Section 10.2 assumed the ocean to have constant density, whereas (see, e.g., Fig. 9.7) the density of the ocean varies horizontally and with depth. In fact, the variation of density with depth helps us out of a conceptual difficulty with our physical interpretation in terms of the Taylor-Proudman theorem on the sphere presented in Section 10.2.3. We described how the Taylor columns of fluid must lengthen in the subtropical gyres to accommodate...

Latitudinal Variations Of Climate

Putting everything together, we can depict the atmospheric wind systems in the upper and lower troposphere schematically as in Fig. 8.15. As we have remarked at various points in this chapter, the structure of the circulation dictates more than just the pattern of winds. In the near-equatorial regions, the convergence of the trade winds is associated with frequent and intense rainfall, as is characteristic of the deep tropics. It is here, for example, that the world's great tropical rainforests...

Planetary Emission Temperature

Hoechst 33342 Wavelength

The Earth receives almost all of its energy from the Sun. At the present time in its evolution the Sun emits energy at a rate of Q 3.87 x 1026 W. The flux of solar energy at the Earth, called the solar constant, depends on the distance of the Earth from the Sun, r, and is given by the inverse square law, So Q 4nr2. Of course, because of variations in the Earth's orbit (see Sections 5.1.1 and 12.3.5) the solar constant is not really constant the terrestrial value TABLE 2.1. Properties of some of...

Freshwater Transport By The Ocean

The ocean and atmosphere must move freshwater from regions of excess rainfall to regions with excess evaporation (see Fig. 11.6). Knowledge of water fluxes and transports in the ocean is important for understanding the global hydrological cycle and climate. For example, variability in fresh water fluxes may have played an important role in the ice ages, as will be discussed in Chapter 12. The plot of evaporation minus precipitation in Fig. 11.6 shows that evaporation exceeds precipitation by...

The equations of fluid motion

Differentiation following the motion 6.2. Equation of motion for a nonrotating fluid 6.2.1. Forces on a fluid parcel 6.5. Integration, boundary conditions, and restrictions in application 6.6. Equations of motion for a rotating fluid 6.6.1. GFD Lab III Radial inflow 6.6.2. Transformation into rotating coordinates 6.6.3. The rotating equations of motion 6.6.4. GFD Labs IV and V Experiments with Coriolis forces on a parabolic rotating table 6.6.5. Putting things on the sphere 6.6.6. GFD Lab...

Convection In Water

Objects that are lighter than water bounce back to the surface when immersed, as has been understood since the time of Archimedes (287-212 BC). But what if the object is a parcel3 of the fluid itself, as sketched in Fig. 4.4 Consider the stability of such a parcel in an incompressible liquid. FIGURE 4.4. A parcel of light, buoyant fluid surrounded by resting, homogeneous, heavier fluid in hydrostatic balance, Eq. 3.3. The fluid above points Ai, A, and A2 has the same density, and hence, as can...

Pressure And Geopotential Height

We have seen that it is warmer in the tropics than at higher latitudes. We will now describe how, through hydrostatic balance, this warmth leads to expansion of tropical air columns relative to polar air columns and hence meridional pressure gradients. It is these pressure gradients that induce fluid accelerations and hence winds. It is customary in meteorology to use pressure rather than height as the primary vertical coordinate. Some conceptual reasons will become clear in Chapter 6. Since,...

Conservation Of Mass

In addition to Newton's laws there is a further constraint on the fluid motion conservation of mass. Consider a fixed fluid volume as illustrated in Fig. 6.4. The volume has dimensions (Sx, Sy, Sz). The mass of the fluid occupying this volume, p Sx Sy Sz, may change with time if p does so. However, mass continuity tells us that this can only (x - j Sx, y - j Sy, z - -g- Szj (x + -g- Sx, y - -g- Sy, z - g- Szj FIGURE 6.4. The mass of fluid contained in the fixed volume, pSx Sy Sz, can be changed...

Baroclinic Instability In The Ocean

In our discussion of the general circulation of the ocean in Chapter 9 it was emphasized that the mean circulation emerges only after long time-averages. Instantaneously the flow is highly turbulent (see, e.g., Figs. 9.19 and 9.22) and the numerical simulation shown in Fig. 9.24. The sloping 9If h is the thickness of the layer across which the density changes by A a, then multiplying f h by A a prf we arrive at isopycnals evident in Fig. 9.7 suggest that there is available potential energy...

A4 Laboratory Experiments

The experiments described throughout this text come to life when they are carried out live, either in demonstration mode in front of a class or in a laboratory setting in which the students are actively involved. Indeed a subset of the experiments form the basis of laboratory-based, hands-on teaching at both undergraduate and graduate level at MIT. As mentioned in Section 0.1, the experiments have been chosen not only for their relevance to the concepts under discussion, but also for their...

The Wind Stress And Ekman Layers

One cannot escape noticing the similarity between the pattern of surface currents in the ocean and that of the low-level winds in the atmosphere. Compare, for example, the pattern of surface elevation of the ocean in Fig. 9.19 with the pattern of surface atmospheric pressure, Fig. 7.27. Winds, through turbulent transfer of momentum across the atmospheric boundary layer, exert a stress on the ocean's surface that drives ocean currents. The surface wind stress can, to a useful degree of accuracy,...

Airsea Fluxes And Surface Property Distributions

Heat, freshwater, and buoyancy fluxes As discussed in Chapter 4, atmospheric convection is triggered by warming at the surface. Vertical mass transport is confined to a few regions of strong updrafts driven by deep convection over the warmest oceans and land masses in the tropics, with broader areas of subsidence in between (see the atmospheric mean meridional circulation plotted in Fig. 5.21). In contrast to the atmosphere, the ocean is forced from above by air-sea fluxes. We therefore...

Differentiation Following The Motion

When we apply the laws of motion and thermodynamics to a fluid to derive the equations that govern its motion, we must remember that these laws apply to material elements of fluid that are usually mobile. We must learn, therefore, how to express the rate of change of a property of a fluid element, following that element as it moves along, rather than at a fixed point in space. It is useful to consider the following simple example. Consider again the situation sketched in Fig. 4.13 in which a...

Dry Convection In A Compressible Atmosphere

Before we can apply the foregoing ideas to atmospheric convection, we must take into account the fact that the atmosphere is a compressible fluid in which p p(p, T) specifically, since the atmosphere closely obeys the perfect gas law, p p RT. For now we will assume a dry atmosphere, deferring consideration of the effects of moisture until Section 4.5. The parcel and environmental pressure, temperature, and density at z z1 in Fig. 4.5 are p1 p(z1), T1 T(z1), and p1 p1 RT1. The real difference...

Vertical Structure Of Pressure And Density

Using the equation of state of air, Eq. 1-1, we may rewrite Eq. 3-3 as In general, this has not helped, since we have replaced the two unknowns, p and p, by p and T. However, unlike p and p, which vary by many orders of magnitude from the surface to, say, 100 km altitude, the variation of T is much less. In the profile in Fig. 3.1, for example, T lies in the range 200-280 K, thus varying by no more than 15 from a value of 240 K. So for the present purpose, we may replace T by a typical mean...

Chemical Composition Of The Atmosphere

Air is a mixture of permanent gases (N2, O2) in constant ratio together with minor constituents (see Table 1.2). The molecular weight of the mixture that makes up air is 28.97, so that 22.4 liters of air at standard temperature and pressure (STP T 273 K and p 1013 h Pa) weighs 28.97 g. The composition of air is a direct consequence of the supply of elements from the Earth's interior and the presence of life on the surface. Photosynthesis by plants makes O2 nitrogenous compounds from living...