Download Global distributions_ temperature

SMS 491/EDU 472
Spring 2007
How is temperature distributed on the Earth and why?
Objective
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Demonstrate understanding of the concept of heat balance
Demonstrate understanding of the processes that affect temperature distributions:
solar radiation, black-body radiation, surface properties (albedo, absorption),
location (e.g., latitude), heat transfer processes (radiation, advection, convection
and conduction)
Become familiar with ocean observing system data (real-time and historical data)
What would be the distribution of temperature on Earth if Earth would have been a
homogeneous ball of rock without fluids (i. e., no oceans and atmosphere)?
Incoming radiation
Total energy received by the sun per unit time:
πR2S, where R is the earth’s radius and S is the solar constant (the annual average
radiative solar flux at the top of the atmosphere) and is equal to 1368 Wm-2. It is referred
to as a constant because it has changed by no more than a few percent over the last few
hundred years (however, note that S has varied over longer geological time scales)
Over all the earth’s surface (divide by the surface area 4πR2), the average amount of
energy received per unit area (m2) per unit time(s)= 1/4S = 344 W m-2.
If the earth’s axis was not tilted the radiation would be maximal at the equator and the
flux received to the poles would be zero (the flux at given latitude is proportional to the
cosine of the sun zenith angle at that latitude, this is known as the cosine ‘effect’). The tilt
of earth results in seasonal variations in the input radiative energy flux.
Activity: open the tool WorldWatcher (this tool can be loaded free from:
http://www.worldwatcher.northwestern.edu/softwareWW.htm)
Click on the ‘energy balance’ icon. Plot the annual average of the incoming solar
radiation and the annual average of the energy absorbed by earth. Compare the values
between the two maps. What may account for the differences?
Not all the energy reaching the earth’s surface is absorbed, part of it is reflected back.
This is quantified by the ratio of incoming to outgoing short wavelength radiation and is
termed the albedo (α). The Earth’s albedo has an average value of 0.3. The albedo has no
units because it is defined as the fraction of the impinging radiation that is reflected.
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It follows that the average amount of solar energy absorbed by the Earth, per unit area per
unit time is:
¼(1-α)S= 240Wm-2.
* Note that we neglect heat from the interior of the earth as it account for less than 0.2%
of the heat provided by the sun.
Activity: Use the WorldWatcher tool to plot the average annual Earth-atmosphere
reflectivity? What causes variations in albedo on the Earth’s surface? Between seasons
(choose two different months and compare them)?
Upward radiation from Earth
Absorbed energy by Earth’s surface will cause the surface to warm up to a temperature
for which it radiates as much energy as it absorbs. To compute the emission from the
Earth’s surface we use the formula for black body radiation: E = σT4
where σ is the Stephan’s-boltzman constant σ= 5.7X10-8 W m-2K-4 (0K = -273oC)
Activity: use the WorldWatcher tool to plot the average annual radiation absorbed by
earth: calculate what would be the temperature of earth reached at equilibrium at the
equator and at the south pole. Compare these values to the map of average annual
Earth’s surface temperature (to convert to Celsius: subtract 32 from oF, divide the
answer by 9 and multiply that answer by 5)
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But, the Earth surface is much warmer. Why?
Simple calculations of the green-house effect:
Now let’s add the atmosphere. The atmosphere is transparent to radiation at short
wavelength (UV and visible light) but partially absorbs at longer wavelength (infra-red).
As downward flux of solar radiation is absorbed by the ground (at short wavelengths), the
ground warms up and emits an upward radiation flux at longer wavelength. Similarly to
the downward flux, the upward emitted flux (U) equals:
U = σT4
A fraction (1≥ e ≥0) of this radiated energy is absorbed by the atmosphere and the
atmosphere heats up and also emits radiation but at longer wavelengths, which we denote
as 2B (a flux B upwards and a flux B downwards back to the Earth).
From the principle of conservation of energy, the upward flux must balance the
downward flux of incoming solar radiation (I):
I = (1-e)U+B = U-B (radiative equilibrium solution)
Î U = σT4 = I/(1-e/2)
Since 1≥e≥0, T is higher than if there would be no atmosphere (the case where e=0).
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Formatted: Portuguese (Brazil)
Activity: use the WorldWatcher tool to plot the mean annual green-house effect. Is this
effect uniform? Why not?
In reality, calculations of fluxes involve many wavebands and the absorption of each
band is calculated separately. Also such models must take into account reflection and
scattering by clouds (which depends on distributions and albedo of clouds)
Not only is Earth’s surface temperature warmer than what is predicted from a simple
radiative model, but also the differences between equator and poles are smaller than
predicted by the simple radiative transport (map of surface temperatures). Why?
Heat transfer by atmosphere and oceans (convection and horizontal transport)
The radiative equilibrium solution presented above does not take into account fluid
motion.
How is this balance affected by fluid motion?
In the vertical: Convection: carries heat and water vapor. Water vapor is an important
player in the radiative balance via its radiation-absorption properties.
Final equilibrium is thus dependent on the BALANCE between radiative and convective
processes.
Convective processes and the hydrological cycle:
Convection depends on the rate at which the temperature of the atmosphere decreases
with height. As a warm parcel of air rises ‘adiabatically’ its temperature decreases as a
result of expansion. If its surrounding is colder it will continue to rise until equilibrium is
reached. Water droplets contained in air have several effects on convection:
- When the amount of water vapor reaches a saturation level (function of height) it
condenses and forms clouds. Clouds reflect and scatter a significant amount of
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incoming radiation and thus affect the total amount of energy absorbed by the
atmosphere.
Water vapor absorbs a fraction of the incoming solar radiation and thus
determines the temperature at the lower atmosphere.
cloud formation results in the release of heat; evaporation results in cooling (this
process accounts for about 75% of the convective transport)
The radiative-convective model we discussed so far assumes only vertical gradients and
convection acts to reduce these gradients.
Latitudinal variation in solar energy flux and radiative absorption result in large
horizontal gradients in temperature. Lateral fluid motion (advection) result (why?) which
tends to reduce these gradients.
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The overall contributions of oceans and atmosphere to energy transport are similar, but
the ocean dominates horizontal transport at 20oN while atmospheric processes dominate
transport at approximately 50oN.
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Activity: In a pure radiative- convective equilibrium the annual average of the space
bound energy should equal the annual average of the absorbed energy. Compare the
two plots (using WorldWatcher). Is that the case? Why?
Activity: what would be the global distribution of surface isotherms in the absence of
horizontal transport? Go to
http://www.osdpd.noaa.gov/PSB/EPS/SST/sst_anal_fields.html. Click to open the 50
KM global analysis climatology. Are isotherms distributed according to your
prediction? Where do they match your prediction and where do they not match? What
are some of the processes responsible for the observed deviations (identify at least 3
processes)?
Reference: Gill, A.E. 1982. Atmosphere-Ocean dynamics. Academic press, Inc.
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