EOS 260 Part II Flashcards
steady state
dx/dt = 0
no change in position with time
stable or unstable
unstable steady state
unstable to a small perturbation- like on top of a hill
starting close to steady state system will diverge away
d2x/dt2>0
non-steady behaviour
transient
stable steady state
starting close to steady state system will converge to it
stable to a small perturbation
d2x/dt2<0
studying steady states
helps us understand the system
two stable steady states
must be separated by an unstable steady state
bistable system
chair, thermohaline circulation, geomagnetic reversals
can be resting in two states, states need not be symmetric with respect to stored energy
defining characteristic of bistability- 2 stable states (minima) are separated by a peak (maximum)
forcing
input to or control parameter affecting the system
will affect the state of the system
not affected itself by the state of the system
examples of forcing
solar forcing- sunlight earth receives
putting consecutively steeper ramps under a chair- force it to tip over
feedback
how the system will respond to a small perturbation or to a change in forcing
2 kinds
stabilizing feedback
negative feedback
diminishes effect of a perturbation, makes change smaller
pushes system back to stable steady state
Couplings
positive- change in A gives a change of same sign in B
shown by an arrow
negative- change in A gives a change of opposite sign in B
shown by line with dot
feedback loops
+1 to positive feeback
-1 to negative feedback
combined effect by multiplying them
most important gas absorbing insolation in atmosphere
H20 vapour
flux density units
W/m^2 = J / m^2 s
incoming solar radiation
341 W/m^2
destabilizing feedback
positive feedback
enhances the effect of a perturbation, makes change larger
pushes system on to next stable steady state after passing unstable steady state
outgoing longwave radiation
239 W/m^2
reflected solar radiation
102 W/m^2
total planetary albedo
outgoing/incoming
102/341 =~ 0.28 ~ 0.3
insolation absorbed by surface
161 W/m^2
average sunlight over whole earth
S/4 ~ 341 W/m^2
S
solar constant
S ~ 1368 W/m^2
relatively constant
where does insolation go
absorbed by atmosphere
absorbed by surface
reflected by surface
reflected by clouds/atmosphere
net energy absorbed by earth
0.9 W/m^2
absorbing ~1 W/m^2 more than it is emitting
where does surface radiation go
thermals evapotranspiration emitted by atmosphere back radiation- emitted back to surface out of atmosphere- through atm. window
rate of temperature change
proportional to energy imbalance ∆F
inversely proport. to system mass x specific heat capacity
dT/dt = ∆F/mc
∆F x area (of earth)
sunlight in the atmosphere
reflected/deflected by clouds, atmospheric molecules
atmospheric molecules
why the sky is blue
area of earth
1.5x10^14 m^2
why did our dt calculation for 2k in the ocean underestimate the time it would take
we found 730yrs
our model assumes ocean mixing, which takes ~1000yrs
what can be seen from calculating dt of certain temperature change in the atmosphere vs. the ocean
ocean takes much longer to heat
global warming is dependent on the ocean
how many seconds in a year
60x60x24x365.25 = 31557600s
2 layers of the atmosphere
troposphere
stratosphere
troposphere
lower layer, T profile set by large scale convection, T decreasing with altitude
stratosphere
upper layer, minimal motion, T set by radiative absorption and emission (O3), increases with altitude
between troposphere and stratosphere
tropopause
before ozone was formed
stratosphere would be constant T with altitude
black body
absorbs all electromagnetic radiation- appears black
emits radiation dependent on wavelength and temperature
Planck function
describes radiative emission of a black body
Stefan-Boltzmann law
integration of the Planck function
F_BB = σ T^4
F is flux, σ is constant, T is in Kelvin
mean earth surface T and F
T = 289 K F_BB = 396 W/m^2
Wein’s displacement law
describes peak emission
as T of BB increases, emission peak moves to shorter λ
λ_max = b / T
λ_max is mx emission (µm), b is 2898µm K
some example λ_max
earth - 10µm (IR)
sun - ~500nm (visible)
largely different spectral regions
visible radiation absorption
not absorbed strongly by atmosphere
most radiation absorbed is at the surface
thermal radiation absorption
absorbed strongly by atmosphere
epsilon
emissivity band of thermal radiation absorption
Earth energy balance
sunlight absorbed
thermal radiation emitted
sunlight absorbed
earth absorbs energy from sun as a circle, some reflected back to space by clouds/atmos/surface
suns energy doesn’t reach all points of earth at one time
absorbing area
π r_e^2
emitting area
4πr_e^2
thermal radiation emitted
earth emits thermal energy from a spherical surface
emitting at all points on earths surface
effective temperature of emission
T_eff
if earth had no atmosphere/greenhouse effect
effective temperature equation
S/4 (1-alpha) = σ T_eff^4
S is solar constant = 1368 W/m^2
alpha is albed = 0.3
attenuation
is the gradual loss in intensity of any kind of flux through a medium
attenuation of radiation in atmosphere
Reflectivity (R), Absorptivity (A), Transmissivity (T)
R + A + T = 1
reflectivity is also called albedo
solar radiation in the atmosphere, attenuation assumptions
R = A = 0
T = 1
‘all insolation goes to E’s surface’
thermal radiation in the atmosphere, attenuation assumptions
R = 0
A ~ 0.75
T ~ 0.25
all IR is absorbed and transmitted, no albedo of IR
Kirchoff’s Law
A_λ = ε_λ
absorptivity = emissivity
only valid where the λ is the same on both sides
grey body
F_grey = ε σ T^4
some fraction of the planck function, a function of every λ
Radiative equilibrium equations
surface
S/4 (1 -alpha) + ε σ Ta^4 = σ Ts^4
atmosphere
ε σ Ts^4 = 2 ε σ Ta^4
rearranging equilibrium equations gives you
Ts^4 = 2Ta^4 surface T is always bigger
a greenhouse gas is
a gas that absorbs thermal radiation
2 most important greenhouse gases
CO2, H20
strength of the greenhouse effect felt by a gas
depends on logarithm of abundance
recall that an increase in 1 is an increased factor of 10 with logarithm
radiative forcing
change in net flux at tropopause (down minus up)
surface temperature changes is proportional to
radiative forcing
Earths surface T without greenhouse effect
~255K
greenhouse effect requires
absorption and re-radiation of thermal energy in atmosphere by greenhouse gases
that atmosphere is colder than surface
strongest radiative forcing change
if you add CH4 you’ll see a stronger effect than CO2 because the base value is so low, log properties, larger change
Climate feedbacks
Planck (temperature) feedback (-)
Water vapour feedback (+)
Ice-Albedo feedback (+)
Planck feedback
solar forcing–> Temp—>outgoing thermal rad—-.temp
increase T = more energy emitted = cools down
water vapour feedback
amplifies T change
solar F–>T—>Atmos. H2O vapour—>greenhouse effect—. outgoing thermal radiation
could lead to runaway greenhouse if Planck feedback stopped working
saturation vapour pressure
e_s is proportional to exp T
equilibrium between liquid and gas
increase water vapour = increase T
e_s is pH2O
greenhouse forcing depend on
change of logarithm of gas abundance
strength of water vapour forcing depends
linearly on temperature change
Ice-albedo feedback
solar F–>solar radiation absorbed—>T—.albedo—.solar radiation absorbed
cold–snow—higher albedo—colder
where there is snow we can see a lower temperature
albedo examples
fresh snow 70-90 sea ice 50-75 desert 25-40 Forest/Grass 10-25 Ocean <10 -70 depending on incident ray
quick changing feedback
ice-albedo
there is snow, or there isnt
tau
thermal optical depth
strength of greenhouse effect
tau = tau_CO2 + tau_H2O
steady state energy balance on daisy world (no atmosphere)
σ T^4 = (1 - alpha)F_s
global albedo is a weighted sum of bare ground, black, white
solar flux on daisyworld
`increases linearly with time
daisyworld albedos
bareground: alpha_bare = 0.5
black: alpha_b = 0.25
white: alpha_w = 0.75
daisies are mesophile
growth rate beat depends on local T
max at 22.5ºC, no growth above 40ºC or below 5ºC
daisy growth
(A)(x)(beta)
x = p - A_w - A_b
p is proportion of planet surface that is fertile
A_w is area covered by white daisies
daisy death
gamma A
daisyworld model
dA_w/dt = A_w ( x beta - gamma) dA_b/dt = A_b ( x beta - gamma)
statement of Gaia hypothesis
Organisms and their material environment evolve as a single coupled system, from which emerges the sustained self regulation of climate and chemistry and habitable state for whatever is the current biota
what does Gaia hypothesis mean
life has controlling influence on physical/chemical climate
life changes atmosphere, maintains habitability through time
theory led to Earth System science
why earth is special
temperature and pressure allow all three phases of water
triple point of phase diagram
all 3 phases exist in equilibrium
pressure on y axis, temperature on x
cryosphere
the frozen water part of the Earth system
southern hemisphere snow
snowy year round, not a lot of year round change
northern hemisphere snow
highly variable, huge variation w/ season, ice albedo changes are a function of the NH
antarctic sea ice cycle
not a lot of variation due to Antarctic circumpolar current
arctic sea ice minimum
september
forming a glacier requires
accumulation of multi-yr ice on land
precipitation (snow) in winter and failure of this to melt fully in summer
consequence of temperature change with altitude in regards to snow/ice
mountains receive most precipitation
snowmelt least likely at high altitude, and on poleward facing slopes
mountain glaciers form first
glacier
valleys, follow topography
ice field
big glacier, still constricted by topography but ‘drapes’ topography, flow direction directed by topography
ice sheet
unrestricted by topography, covers it and goes where it wants
ice shelf
floats at edge of ice sheet/glacier
net ice build up
accumulation
net ice loss
ablation
above glacier equilibrium line
snow > melt
accumulation zone
below glacier equilibrium line
melt > snow
ablation zone
mountain glaciers in the absence of melt
can grow to form ice sheets
ice sheet-altitude feedback
growth of ice sheet–raises altitude of ice surface– surface temperature is colder– melt inhibited
positive feedback
ice sheet flow
from centre of ice dome (high pt.) outward
thicker ice sheet
more likely to slide at base
movement of ice as a function of base T
base > 0º, melt, wet base, glacier can slide, flow quickly, lubricated by melt-water percolated to bottom
base < 0º, bed frozen, glaciers flow more slowly, movement requires deformation
warming ice sheet
speed up flow–loss of altitude–warmer T–more melt
positive feedback
glacial records
glacial valleys, moraines, striations, tillites, loess
ice rafted debris
piece breaks off of iceberg–flows away– starts melting– drops sediment– can deform bottom sediment
glacial loess
When glaciers grind rocks to a fine powder, loess can form. Streams carry the powder to the end of the glacier. This sediment becomes loess
large ice cap instability
if ice reaches mid latitudes positive feedback will lead to global glaciation
from O-D energy balance model with ice-albedo feedback
small ice cap instability
if ice decreases too much it will all melt, no glaciation
ice sheets don’t get smaller, they collapse
north american ice sheets
lost: Laurentide, Cordillian, Scandanavian
remain: greenland
Phanerozoic/Proterozoic glaciations
Oligocene-Present (poles) Devonian, Cretaceous, Permian Ordovician- Siluria Cryogenian (Neoproterozoic) Siderian (paleoproterozoic)
faint young sun paradox
with lower S glaciation would be deep (with todays atmospheric composition)
yet geological evidence shows less glaciation earlier in history
stronger greenhouse?
isotope
same number of protons, different number of neutrons, same atomic number, different mass, same chemical properties, different physical properties
oxygen isotopes
16O - 99.76%
17O - 0.04%
18O - 0.2%
16,18 most commonly used for palaeoclimate
hydrogen isotopes
1H - 99.984%
2H - 0.016%
2H
deuterium ‘D’
isotopologues
different forms of the same molecules, varying by isotopic composition
molecules with different isotopes, multiple heavy isotopes in one molecule, rare
ex. H2O with 0,1,2, deuterium
most common water isotopologues
(1H)2(16O)
(1H)2(18O)
(1H)(2H)(16O) - HDO
in order of commonality
isotopic ratio
R = rare X / common X
ex. D: R = D/H = 0.016/99.984 = 0.00016
problem with isotope ratio
variations are very small numbers
delta notation ratio
δX = 1000 ((Rsample-Rstandard)/Rstandard)
units are ‘permil’ parts per thousand
δD =
1000 [ ( (D/H)sample - (D/H)smow ) / (D/H)smow ]
SMOW
standard mean ocean water
standard for H and O for ice sheets
isotopic mass balance
m_tot = m_1 + m_2
m_tot δ_tot = m_1 δ_1 + m_2 δ_2
δ18Osmow =
0%o
negative delta isotope values
depleted in 18O
preferentially left behind
the more negative, the colder
saturation vapour pressure
describes amount of water vapour in equilibrium with liquid water
saturation vapour pressure of isotopologues
lower for heavier isotop., light isotopes evaporate preferentially
e_s((1H)2(16O)) is 1% lower than e_s((1H)2(18O))
e_s(HDO) is 10% lower than e_s((1H)2(16O)
water vapour isotopes compared to ocean water
water vapour is isotopically light
δ18O_wv < δ18O_ocean
δD_wv < δD_ocean
precipitation is isotopically heavy relative to water vapour
δ18O_wv < δ18O_precip
δD_wv < δD_precip
as temperature decreases from the source region of moisture
increasingly higher fractions of the atmospheric water vapour have precipitated out
remaining water becomes increasingly isotopically light and further precipitation will be lighter
isotopic concentration of precipitate a function of
temperature at which precipitation occurs
precipitation is isotopically lighter
further from the source
at higher altitudes
why ice cores are drilled at the summit of an ice cap
reduces distortion due to ice flow
stratigraphy of ice core with depth
~54m down- hard to see layers, use conductivity based on dust
~1800m down- clear layers can be seen
~3000m down- lots of sediment, layers may be lost
ability to resolve layers decreases with depth
ways to date stratigraphic layers
δ18O variation with seasonal cycle due to T variation
microparticle/glaciergeochemistry seasonal cycles
electrical conductivity- seasonal variations of contaminant load
reference horizons- radioactives, volcanic ash
trade off between time resolution of ice core and length of record
higher snow accumulation rate = better time resolution
faster accumulation = faster flow, shorter time record
longer record, lower resolution ex.greenland
why layers are thinner down ice core
pressure
why might δD be better than δ18O in ice
mass differences
H 1/2 (half of mass)
O 16/18
δD versus age graph
less (-), warmer T’s, interglacials
glacials last longer than interglacials
packed snow
firn
bubble formation in glacier
pressure of firn compresses packed snow into ice ~50m
100’s of years at warm, high accumulation
1000’s of yrs at cold, interior, low accumulation
age of air in ice
younger than ice itself (because they take so long to close)
and they close at different times
pacemaker of ice-ages
insolation changes (which affect ice volumes)
isotopes of ice sheets
accumulation of ice sheet removes light isotopes
ocean water become isotopically heavy
foraminifera
CaCO3 tests, must determine benthic vs. planktic
how forams represent ice volume
18O concentrated in CaCO3 relative to water (more with colder water), bust be planktonic (benthic waters don’t show much T variation)
marine δ18O graph
y-axis is opposite- heavy = high ice volume = cold
Pleistocen glaciation
regular glacial-interglacial cycles
before 700ka periodicity = 40ka
after 700ka periodicity = 100ka
change in glacial-interglacial periodicity
mid-Pleistocene climate transition
why are glacial studies better from antarctic
right on the pole-harder to melt ice sheet, more information contained in that
arctic ice is away from the pole, higher insolation
Croll-Milankovitch theory
Eccentricity
Axial tilt
Precession
eccentricity
how elliptical earths orbit it
eccentricity periodicity
100,000yrs
what eccentricity does
changes distribution of solar energy throughout year
perihelion
closest to sun (right now in NH Jan)
earth moving faster at this point of orbit to cover same amount of area
axial tilt
obliquity, the degree to which the axis is tilted changes
axial tilt periodicity
41,000yrs
axial tilt implications
changes strength of season
aphelion
earth farthest from sun
if obliquity were 0
no seasons
precession
wobble, change in where N/S axis points
precession periodicity
23,000 yrs
precession implications
relative strength and length of seasons
Croll-Milankovitch theory explains timing of glaciations
NH summer insolation is critical in determining ice volume, summer insolation determines whether glaciers survive ice-albedo feedback, most land mass- largest changes in ice extent
organic carbon dominantly fixed by
oxygenic photosynthesis
CO2 + H2O + hv —- CH2O + O2
inorganic matter reduced to organic matter
aerobic respiration
CH2O + O2 — CO2 + H2O
photosynthesis + aerobic respiration
closed cycle
decomposition of organic carbon in oxygen low environment
fermentation followed by methanogenesis
net: 2CH2O — CO2 + CH4
inorganic carbon
HCO3 -
CO3 2-
H2CO3
counter reaction to fermentation/methanogenesis
CH4 + 2O2 – CO2 + 2H2O
again, closed system
carbon reservoir cycling
biological reservoirs cycle quick
geochemical reservoirs cycle slow
atmospheric CO2 reservoir
760
photosynthesis takes 60 out
60 goes back in, fast cycling
residence time
tau = steady state reservoir size / flux
ex. 760 / 60 = ~13 yrs
basic structure of the ocean
2 layers: Mixed layer, deep ocean
mixed layer
~100m, geochemical equilibrium with atmosphere, well mixed by wind
ocean gradients
thermocline
chemocline
light penetration
thermocline
sudden small T decrease then, decreases gradually with depth down to ~100m where it reaches the minimum and stays ~constant
chemocline
ex. nutrient availability, abrupt decrease with depth
light penetration gradient
gradual decrease, area light penetrates = photic zone
Henry’s law
assuming air-sea surface gas exchange in equilibrium [x] = k_H px [x] dissolved molar concentration (M) k_H henrys law constant (M/atm) px partial pressure (atm)
1atm =
101325 pa
gases are more soluble in
cold water
DIC reservoirs, smallest to biggest
H2CO3
CO2
CO3 2-
HCO3 -
carbonate chemistry
collective chemistry of DIC species
conserved oceanic carbon quantities
DIC
Alkalinity
DIC =
[CO2] + [H2CO3] + [HCO3 -] + [CO3 2-]
Alkalinity
expresses charge balance, net + charge from conservative ions balanced by net - charge of weak acids
circumneutral conditions in ocean
pH > 4
pH =
- log [H+]
conservative ions
ions that don’t do much chemistry at ciarcumneutral conditions in ocean, salts, net +
[Na+] - [Cl-] + 2[Mg 2+] + 2[Ca 2+] > 0
Alkalinity, Alk =
[HCO3 -] + 2[CO3 2-] - [H+]
DIC reactions
CO2 + H20 ——– H2CO3
H2CO3 ——– H+ + HCO3 -
HCO3 - ——– H+ + CO3 2-
increasing pCO2
increases [CO2] – increases [H2CO3] — increases [H+] and [HCO3-] — increases [HCO3-] —- decreases [CO3 2-]
increased hydrogen ions, decreases pH, ocean acidification
why do we subract [Cl-] in conservative ion equation
because we are adding up the positive charges
pCO2 in DIC vs. Alkalinity graph
below ~where we are now (~0) - not possible
increasing in DIC = increased pCO2 (up to ~6µatm)