1. Radiation Basics and the General Circulation
SO 254 – Spring 2017

2. Earth-Sun Geometry
~23.5°
Arctic Circle (~66.5° N)
The earth’s axis is tilted at an angle of ~23.5° (why we have seasons)
Boreal (N.H.) Winter Solstice (~21 Dec)
Sun directly overhead Tropic of Capricorn
Sun never rises above Arctic Circle
Sun never sets below Antarctic Circle
Tropic of Capricorn (~23.5° S)
Tropic of Cancer (~23.5° N)
Antarctic Circle (~66.5° S)
Vernal Equinox (~20 March)
The term Austral is used in reference to the S.H.
Sun directly overhead equator
Boreal Summer Solstice (~21 Jun)
(the Austral summer is concurrent with the Boreal winter)
Sun directly overhead Tropic of Cancer
Sun never sets above Arctic Circle
Sun never rises below Antarctic Circle
Autumnal Equinox (~22 September)
Sun directly overhead equator

3. Solar radiation (in brief)
Radiation from the sun may be characterized by its equivalent blackbody temperature which, in accordance with Planck’s Law of blackbody radiation, determines its spectrum. The empirically derived Planck function is:
𝐸 𝜆 ∗ = emittance or flux per unit wavelength (W m −2 μm −1 )
𝜆= wavelength (μm) where 1 μm= 10 −6 m
𝑇= absolute temperature (K) 𝑐 1 / 𝑐 2 = constants
𝐸 𝜆 ∗ = 𝑐 1 𝜆 5 𝑒 𝑐 2 𝜆𝑇 −1
The spectrum for a particular temperature is illustrated by its Planck curve which plots emittance as a function of wavelength
𝑑 𝐸 𝜆 ∗ 𝑑𝜆 =0
How mathematically would you determine the wavelength where 𝐸 𝜆 ∗ is a maximum?
Differentiate the Planck function with respect to 𝜆, set the derivative equal to zero, and solve for 𝜆

4. Solar radiation (in brief)
How mathematically would you determine the wavelength where 𝐸 𝜆 ∗ is a maximum?
𝑑 𝐸 𝜆 ∗ 𝑑𝜆 =0
Differentiate the Planck function with respect to 𝜆, set the derivative equal to zero, and solve for 𝜆
This process yields Wein’s Law:
𝜆 max = 𝑎 𝑇
where 𝑎=2897 μm K
Solar radiation is concentrated in the visible spectrum (0.4−0.65 μm). What would be an estimate for the solar surface temperature?
𝑇≅5780 K
(this is pretty close)

5. Solar radiation (in brief)
How mathematically would you find the total emittance (or “flux density”) from the sun at all wavelengths?
Integrate 𝐸 𝜆 ∗ over all values of 𝜆
This produces the Stefan-Boltzmann law:
𝐸 ∗ =𝜎 𝑇 4
Where 𝜎=5.67× 10 −8 W m −2 K −4 is the Stefan-Boltzmann constant
Solar radiation received at the Earth (primarily visible) is referred to as shortwave radiation or INcoming SOLar radiATION (insolation)
Solar emittance attenuates through spreading loss as it travels to earth approximately via a formulation of the inverse square law…

6. Solar radiation (in brief)
The flux density 𝐸 ∗ at any two distances 𝑑 from a point source is given by:
𝐸 ∗ 1 𝑑 1 2 = 𝐸 ∗ 2 𝑑 2 2
Calculate the solar flux density reaching the orbital radius of Earth (1.495× km) given a solar surface temperature of 5780 K and solar radius of 6.96× km
From the Stefan-Boltzmann law, 𝐸 ∗ 1 (at the solar surface) is ~6.328× W m −2
Flux density decreases proportionally with the inverse of the square of the distance from the source
𝐸 ∗ ∝ 1 𝑑 2
Thus 𝐸 ∗ 2 (at Earth’s orbit) is ~1372 W m −2

7. Terrestrial radiation (in brief)
Some incoming solar radiation is reflected back into space vice being absorbed by the Earth system
The ratio of reflected to incoming solar radiation is called albedo 𝐴 and is given by:
𝐴= 𝐸 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝐸 𝑖𝑛𝑐𝑜𝑚𝑖𝑛𝑔
Albedo varies by surface:
Clouds, ice, and snow are particularly good reflectors
Global average albedo is about 30%

8. Terrestrial radiation (in brief)
Given the average Earth albedo of 30%, we can calculate the equivalent blackbody temperature of the Earth if we assume radiative equilibrium (i.e., no net gain or loss in energy due to radiative transfer)
Solar flux density: 𝐸 ∗ 𝑠𝑜𝑙𝑎𝑟 =1372 W m −2
𝐸 ∗ 𝐸𝑎𝑟𝑡ℎ
Solar radiation is intercepted over the area 𝜋 𝑅 𝐸 2 and terrestrial radiation is emitted over the area 4𝜋 𝑅 𝐸 2
𝐸 ∗ 𝑠𝑜𝑙𝑎𝑟
( 𝑅 𝐸 = radius of the Earth)
Using Stefan-Boltzmann’s law: 𝐸 ∗ 𝐸𝑎𝑟𝑡ℎ =𝜎 𝑇 4
As 𝜆 𝑚𝑎𝑥 is in the infrared, terrestrial radiation is referred to as longwave radiation
Here, 𝐸 ∗ 𝐸𝑎𝑟𝑡ℎ = 1372(1−0.3) 4 =240 W m −2
Solving for 𝑇 gives:
𝑇≅255 K

9. Surface Radiation Budget
The net radiative flux 𝐹 ∗ at a point on Earth’s surface has contributions from:
Shortwave radiation (insolation) 𝐾↓
Atmospheric longwave radiation 𝐼↓
Reflected shortwave radiation 𝐾↑
Terrestrial longwave radiation 𝐼↑
𝐹 ∗ =𝐾↓+ 𝐾↑+ 𝐼↓+ 𝐼↑
Typical diurnal cycle (fluxes are positive upward)
night

10. Surface Radiation Budget
Lower sun angle
What accounts for the difference here?

11. − =
The surplus of incoming solar radiation over outgoing longwave radiation at low latitudes and the deficit at high latitudes results in differential heating
This process drives the global-scale general circulation of winds

12. polar subpolar extratropical subtropical tropical Terminology
meriodonal
90°W
60°W
Lines of latitude are parallels
60°N
subpolar
East/West winds are zonal winds
zonal
meriodonal
subtropical
Lines of longitude are meridians
30°N
North/South winds are meriodonal winds
tropical
zonal 0°
<𝟑𝟎° low latitudes
𝟑𝟎−𝟔𝟎° mid-latitudes
>𝟔𝟎° high latitudes

13. pressure gradient force
Terminology
Local maxima in the pressure field are high pressure centers or highs (H)
Local minima in the pressure field are low pressure centers or lows (L)
pressure gradient force H L
The applied pressure gradient force causes wind to blow from high to low pressure though other forces deflect air motion to varying degrees
On larger scales, the rotation of the Earth imparts a significant deflection on winds

14. H L H L Terminology Northern Hemisphere
Anticyclonic circulation (clockwise)
Around low pressure, winds circulate cyclonically (in the same sense as Earth’s rotation looking down on the pole) + NP
Areas of low pressure are also referred to as cyclones
Cyclonic circulation (counterclockwise) L
Southern Hemisphere
Around high pressure, winds circulate anticyclonically (opposite the sense of Earth’s rotation looking down on the pole) H
Anticyclonic circulation (counterclockwise)
Areas of high pressure are also referred to as anticyclones + SP
Cyclonic circulation (clockwise) L

15. General Circulation – “aqua Earth” (sun overhead equator)
Differential heating causes rising motion within a few degrees of the equator
This promotes surface low pressure and equatorward flow at low levels which is deflected westward by Earth’s rotation H H
Hadley
Rising air encounters the tropopause where it is inhibited from further rising by strong static stability in the stratosphere L L
Rising air diverges poleward, is deflected eastward by Earth’s rotation, and sinks in the subtropics promoting surface high pressure and closing the loop
These mirror-image cells are called Hadley cells

16. General Circulation – “aqua Earth” (sun overhead equator)
Surface flow spreading poleward out of the descending branch of the Hadley cell rises again at higher latitudes where it subsequently diverges
Polar
Ferrel H
Hadley
This process forms a mid-latitude Ferrel cell which has a vertical circulation counter to the Hadley cell and a high-latitude polar cell L

17. General Circulation – “aqua Earth” (sun overhead equator)
At the surface, the low-level winds of the Hadley cell called trade winds converge heat and moisture where they meet along the intertropical convergence zone (ITCZ)
trade
winds
Surface winds along the ITCZ are generally light (doldrums)
I T C Z
As this air rises, it cools and condenses moisture forming clouds and precipitation
The sinking air in the descending branch of the Hadley cell, on the other hand, is characteristically dry and forms subtropical highs where surface winds are also generally light (horse latitudes)

18. Surface Circulation – “aqua Earth” (sun overhead equator)
Westerlies
At the surface in the mid-latitudes, winds vary in direction with the passage of extratropical cyclones which generally move eastward in a prevailing westerly flow (the westerlies)
Polar easterlies H L
Subpolar low H H
Subtropical high
NE trade winds L
ITCZ
Under the rising branch of the Ferrel cell are subpolar lows
SE trade winds H
Subtropical high
Near each pole is a climatological polar high
Westerlies L
Subpolar low
Between the polar high and the subpolar lows is a region of winds called the polar easterlies

19. Upper-level Circulation – “aqua Earth” (sun overhead equator)
In the upper-troposphere, easterly winds and high pressure prevail above the ITCZ whereas westerly winds prevail elsewhere L
polar
jet
subtropical
jet
A region of strong westerly winds called the subtropical jet overlies the descending branch of the Hadley cell H H H
An additional polar jet is present at higher latitudes and supports Rossby waves which arise from instabilities in the flow
subtropical
jet
polar
jet
A polar low is present at each pole in the upper-troposphere

20. General Circulation – “aqua Earth” (Boreal summer)
Max insolation is displaced into the summer hemisphere and the Hadley cells become asymmetric as the ITCZ migrates northward (~10° latitude)
The winter hemisphere’s Hadley cell becomes the major cell with stronger circulation due to the greater zonal temperature contrast
The vigorous circulation in the major cell acts to balance extreme temperature contrasts by transporting significant heat away from the tropics
The setup is reversed in the Austral summer

21. General Circulation – “real Earth”
polar easterlies
Over the oceans, surface winds are very similar to “aqua Earth” L
The subtropical high pressure belt, however, is not continuous but forms distinct subtropical anticylones centered over the mid-oceans
westerlies H
trade winds
These carry (or advect) cooler, dryer air equatorward on the eastern side of the ocean basins and advect warmer, more humid air into the mid-latitudes on the western side
In the North Atlantic, these are known as the Azores (or Bermuda) high and the Icelandic low
The high is most discernable in summer and the low is strongest in winter
The subpolar low pressure belt likewise forms distinct mid-ocean cyclones

22. General Circulation – “real Earth”
In the Indian Ocean basin the presence of landmasses has a pronounced influence on observed wind circulations
In the boreal summer, intense heating over Asia (relative to the tropical ocean) causes ascent and disrupts the northern Hadley cell circulation eliminating the subtropical anticyclone
In the boreal winter, the tropical ocean is warm (relative to cooling over Asia) causing the pattern to reverse H H
This seasonal reversal of surface winds is called the monsoon circulation

23. General Circulation – “real Earth”
Which of these profiles represents the December- January-February (DJF) average of global surface winds?
Surface winds
Surface winds

24. December-January-February (DJF) averages
Aleutian low
Icelandic low
westerlies
Indian
monsoon
ITCZ
subtropical anticyclones
Surface winds

25. December-January-February (DJF) averages
Farrel cells
Hadley cells
Surface winds

26. June-July-August (JJA) averages
Azores/Bermuda high
Indian
monsoon
westerlies
ITCZ
Surface winds