Download Lesson 02

Radiation Basics and
the General Circulation
SO 254 – Spring 2017
Earth-Sun Geometry
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
•
•
•
•
Vernal Equinox (~20 March)
Sun directly overhead equator
The term Austral is used in
the S.H.
Borealreference
Summer to
Solstice
(~21 Jun)
(the
is Tropic
concurrent
SunAustral
directlysummer
overhead
of Cancer
with the
Boreal
Sun never
sets
abovewinter)
Arctic Circle
Sun never rises below Antarctic Circle
Cancer
(~23.5° N)
Arctic~23.5°
Circle
(~66.5° N)
Tropic of
Capricorn
(~23.5° S)
Antarctic
Circle
(~66.5° S)
Autumnal Equinox (~22 September)
• Sun directly overhead equator
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:
𝑐1
∗
𝐸𝜆 =
𝜆5 𝑒 𝑐2
𝜆𝑇
−1
𝐸𝜆 ∗ = emittance or flux per unit wavelength (Wm−2 μm−1 )
𝜆 = wavelength (μm) where 1 μm = 10−6 m
𝑇 = absolute temperature (K) 𝑐1 /𝑐2 = constants
The spectrum for a particular temperature is
illustrated by its Planck curve which plots
emittance as a function of wavelength
How mathematically would you determine the
wavelength where 𝐸𝜆 ∗ is a maximum?
Differentiate the Planck function with respect to 𝜆,
set the derivative equal to zero, and solve for 𝜆
𝑑𝐸𝜆 ∗
=0
𝑑𝜆
Solar radiation (in brief)
How mathematically would you determine the
wavelength where 𝐸𝜆 ∗ is a maximum?
Differentiate the Planck function with respect to 𝜆,
set the derivative equal to zero, and solve for 𝜆
This process yields Wein’s Law:
𝑎
𝜆max =
where 𝑎 = 2897 μm K
𝑇
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)
𝑑𝐸𝜆 ∗
=0
𝑑𝜆
Solar radiation (in brief)
How mathematically would you find the total
emittance (or “flux density”) from the sun at all
wavelengths?
Integrate 𝐸𝜆 ∗ over all values of 𝜆
This produces the Stefan-Boltzmann law:
𝐸∗
=
𝜎𝑇 4
Where 𝜎 = 5.67 × 10−8 Wm−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…
Solar radiation (in brief)
The flux density 𝐸 ∗ at any two distances 𝑑 from a point source is given by:
𝐸 ∗1 𝑑1 2 = 𝐸 ∗ 2 𝑑2 2
Calculate the solar flux density
reaching the orbital radius of
Earth (1.495 × 108 km) given a
solar surface temperature of
5780 K and solar radius of
6.96 × 105 km
Flux density decreases proportionally with
the inverse of the square of the distance
from the source
1
∗
𝐸 ∝ 2
𝑑
From the Stefan-Boltzmann law,
𝐸 ∗1 (at the solar surface) is
~6.328 × 107 Wm−2
Thus 𝐸 ∗ 2 (at Earth’s orbit) is
~1372 Wm−2
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:
𝐸𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑
𝐴=
𝐸𝑖𝑛𝑐𝑜𝑚𝑖𝑛𝑔
Albedo varies by surface:
Clouds, ice, and
snow are particularly
good reflectors
Global average
albedo is about 30%
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 Wm−2
Solar radiation is intercepted over the area 𝜋𝑅𝐸 2
and terrestrial radiation is emitted over the area
(𝑅𝐸 = radius of the Earth)
4𝜋𝑅𝐸 2
𝐸 ∗ 𝐸𝑎𝑟𝑡ℎ
𝐸 ∗ 𝑠𝑜𝑙𝑎𝑟
Using Stefan-Boltzmann’s law: 𝐸 ∗ 𝐸𝑎𝑟𝑡ℎ = 𝜎𝑇 4
Here, 𝐸 ∗ 𝐸𝑎𝑟𝑡ℎ =
1372(1−0.3)
4
Solving for 𝑇 gives:
𝑇 ≅ 255 K
= 240 Wm−2
As 𝜆𝑚𝑎𝑥 is in the infrared,
terrestrial radiation is referred to
as longwave radiation
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
night
Surface Radiation Budget
Lower sun angle
What accounts for the
difference here?
−
=
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
Terminology
polar
subpolar
extratropical
subtropical
tropical
Lines of latitude are parallels
60°N
East/West winds are zonal winds
30°N
Lines of longitude are meridians
North/South winds are meriodonal
winds
0°
< 𝟑𝟎° low latitudes
𝟑𝟎 − 𝟔𝟎° mid-latitudes
> 𝟔𝟎° high latitudes
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)
H
pressure gradient
force
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
Northern Hemisphere
H
+
Terminology
Anticyclonic
circulation
(clockwise)
Around low pressure, winds circulate
cyclonically (in the same sense as
Earth’s rotation looking down on the pole)
Cyclonic circulation
(counterclockwise)
Areas of low pressure are also referred to
as cyclones
NP
L
Southern Hemisphere
H
+
SP
L
Anticyclonic
circulation
(counterclockwise)
Cyclonic circulation
(clockwise)
Around high pressure, winds circulate
anticyclonically (opposite the sense of
Earth’s rotation looking down on the pole)
Areas of high pressure are also referred
to as anticyclones
General Circulation – “aqua Earth” (sun overhead equator)
Differential heating causes rising motion
within a few degrees of the equator
H
L
H
L
H
H
L
H
This promotes surface low pressure and
equatorward flow at low levels which is
deflected westward by Earth’s rotation
L
H
Rising air encounters the tropopause
where it is inhibited from further rising by
strong static stability in the stratosphere
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
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
H
L
H
This process forms a mid-latitude Ferrel
cell which has a vertical circulation
counter to the Hadley cell and a highlatitude polar cell
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)
I
T
C
Z
Surface winds along the ITCZ are
generally light (doldrums)
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)
Surface Circulation – “aqua Earth” (sun overhead equator)
H
L
H
L
H
H
L
H
Polar easterlies
L
L
H
H
L
L
H
Subpolar low
Westerlies
Subtropical high
NE trade winds
ITCZ
SE trade winds
Subtropical high
Westerlies
Subpolar low
Polar easterlies
At the surface in the midlatitudes, winds vary in
direction with the passage of
extratropical cyclones which
generally move eastward in a
prevailing westerly flow (the
westerlies)
Under the rising branch of the
Ferrel cell are subpolar lows
Near each pole is a
climatological polar high
Between the polar high and
the subpolar lows is a region
of winds called the polar
easterlies
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
jet
subtropical
H
H
H
jet
subtropical
L
A region of strong westerly winds called
the subtropical jet overlies the
descending branch of the Hadley cell
An additional polar jet is present at
higher latitudes and supports Rossby
waves which arise from instabilities in the
flow
A polar low is present at each pole in the
upper-troposphere
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
General Circulation – “real Earth”
polar easterlies
L
westerlies
H
trade
winds
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
Over the oceans, surface winds are very
similar to “aqua Earth”
The subtropical high pressure belt,
however, is not continuous but forms
distinct subtropical anticylones centered
over the mid-oceans
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
The subpolar low pressure belt likewise
forms distinct mid-ocean cyclones
General Circulation – “real Earth”
H
H
H
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
This seasonal reversal of surface winds
is called the monsoon circulation
General Circulation – “real Earth”
Surface winds
Surface winds
Which of these profiles
represents the
December- JanuaryFebruary (DJF)
average of global
surface winds?
December-January-February (DJF) averages
Aleutian low
Icelandic low
Indian
monsoon
westerlies
ITCZ
Surface winds
subtropical
anticyclones
December-January-February (DJF) averages
Farrel cells
Hadley cells
Surface winds
June-July-August (JJA) averages
Indian
monsoon
Azores/Bermuda
high
ITCZ
westerlies
Surface winds