lecture 2: structure and composition of the atmosphere and ... · lecture 2: structure and...

The atmosphereEquation of state and hydrostatic balance

The ocean

Lecture 2:Structure and Composition of the Atmosphere and Ocean

Jonathon S. Wright

[email protected]

28 February 2017


The ocean

The atmosphereTemperature structureMajor constituentsGreenhouse gases

Equation of state and hydrostatic balanceThe atmospheric equation of stateHydrostatic balance

The oceanCompositionEquation of stateVertical structure


The ocean

Temperature structureMajor constituentsGreenhouse gases

180 200 220 240 260 280 300Temperature [K]

0

20

40

60

80

100

Alti

tude

abo

ve s

ea le

vel [

km]

Troposphere

Stratosphere

Mesosphere

Thermosphere

Tropopause

Stratopause

Mesopause

data from 1976 US Standard Atmosphere

http://en.wikipedia.org/wiki/U.S._Standard_Atmosphere


The ocean


The Lapse Rate

Γ = −dTdz


The ocean


Gas Percent by volume

Nitrogen (N2) 78.08%Oxygen (O2) 20.95%Argon (Ar) 0.93%Water Vapor (H2O) 0.00001–4.0%Carbon Dioxide (CO2) 0.039%Neon (Ne) 0.0015%Helium (He) 0.0005%Methane (CH4) 0.00018%Ozone (O3) 0.000003–0.001%Krypton (Kr) 0.0001%


The ocean


190 200 210 220 230 240 250 260 270 280 290 300Temperature [K]

200

400

600

800

1000

Pre

ssur

e [h

Pa]

Mean air temperature

NH high latitudes (60-90°N)NH mid latitudes (30-60°N)NH subtropics (15-30°N)Tropics (15°S-15°N)SH subtropics (15-30°SSH mid latitudes (30-60°S)SH high latitudes (60-90°S)

0.0 2.5 5.0 7.5 10.0 12.5 15.0

Specific humidity [g kg−1]

200

400

600

800

1000

Pre

ssur

e [h

Pa]

Mean atmospheric water vapor content

data from CFSR

Water Vapor

I a chemically active greenhouse gas

I critical for energy transport

I temperature determines upper limit

http://cfs.ncep.noaa.gov/cfsr/


The ocean


1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015Year

320

340

360

380

400

CO

2 co

ncen

tratio

n [p

pm]

Atmospheric CO2 at Mauna Loa

J F M A M J J A S O N D4

2

0

2

4

data from NOAA ESRL

Carbon Dioxide

I another important greenhouse gas

I primary source of carbon for photosynthesis

I affects ocean acidity

I well mixed

http://www.esrl.noaa.gov/gmd/ccgg/trends/


The ocean


1985 1990 1995 2000 2005 2010Year

1600

1650

1700

1750

1800

1850

CH

4 co

ncen

tratio

n [p

pb]

Atmospheric CH4 (NOAA Marine Boundary Layer Reference)

data from NOAA ESRL

Methane

I also a greenhouse gas

I natural and anthropogenic sources

I important source of water vapor in the stratosphere

http://www.esrl.noaa.gov/gmd/ccgg/mbl


The ocean


data from OMI

Ozone

I absorber of both solar and infrared radiation

I chemically active

I important for life, but harmful to health

http://disc.sci.gsfc.nasa.gov/datacollection/OMTO3d_V003.html


The ocean

The atmospheric equation of stateHydrostatic balance

p = ρRdT

Assumptions: I motion of air molecules is random

I individual molecules interact rarely

I air is dry: no water vapor

Atmospheric equation of state


The ocean


0 200 400 600 800 1000Pressure [hPa]

0

20

40

60

80

100

Alti

tude

abo

ve s

ea le

vel [

km]

0 0.4 0.8 1.2Air density [kg m−3]

0

20

40

60

80

100




The ocean


pressure gradient force:

[p−

(dp

dz

)δz

]δA− pδA = −

(dp

dz

)δzδA

gravitational force: gρδAδz g = −(

1ρdpdz

)δz

δA

Hydrostatic balance


The ocean


g = −1

ρ

dp

dz

ρ =p

RdT

hydrostatic balance

equation of state

scale heightdp

p= −dz

H, H =

RdT

g

If temperature is constant with height, then so is H:

p = pse(− z/H)

Applying hydrostatic balance


The ocean


0 200 400 600 800 1000Pressure [hPa]

0

20

40

60

80

100

Alti

tude

abo

ve s

ea le

vel [

km]

0 0.4 0.8 1.2Air density [kg m−3]

0

20

40

60

80

100

p = pse(− z/H) ρ = p

RdT




The ocean


g = −1

ρ

dp

dz

m = ρdz

hydrostatic balance

mass of a layer

m =dp

g

The pressure at the top of the atmosphere is zero, so the mass per unit area is:

M =psrf − ptoa

g=psrf − 0

g=psrfg

Applying hydrostatic balance


The ocean

CompositionEquation of stateVertical structure

constituent ion mass mixing ratio percentage ofin seawater [g kg−1] global salt

Chloride (Cl−) 19.215 54.96%Sodium (Na+) 10.685 30.58%

Sulphate (SO2−4 ) 2.693 7.70%

Magnesium (Mg2+) 1.287 3.69%Calcium (Ca2+) 0.410 1.17%Potassium (K+) 0.396 1.13%Bicarbonate (HCO−

3 ) 0.142 0.41%Bromide (Br−) 0.067 0.19%Boric acid (H3BO3) 0.026 0.07%


The ocean


Equation of state for seawater

I pressure

I temperature

I density

I salinity

No general theory for liquids

Must be determined by fitting a function to measurements


The ocean


0 250 500 750 1000 1250 1500 1750 2000Pressure [dbar]

0

500

1000

1500

2000

Dep

th [m

]

Mean pressure (World Ocean Atlas 2009)


pressure increases at ∼1 atm per 10 m

data from WOA2009

http://www.nodc.noaa.gov/OC5/WOA09/pr_woa09.html


The ocean


5 0 5 10 15 20 25 30Temperature [°C]

0

500

1000

1500

2000

Dep

th [m

]

Mean temperature (World Ocean Atlas 2009)


below 0◦C in high latitudes

thermocline

mixed layer

data from WOA2009



The ocean


31 32 33 34 35 36Salinity [psu]

0

500

1000

1500

2000

Dep

th [m

]

Mean salinity (World Ocean Atlas 2009)


data from WOA2009



The ocean


σ(T, p, S) = ρ(T, p, S)− 1000kgm−3

generally report density relative to density of pure water:

Density of seawater

I pressure

I temperature

I salinity


The ocean


20 22 24 26 28 30 32 34 36 38 40Density [kg m−3]

0

500

1000

1500

2000

Dep

th [m

]

Mean density (World Ocean Atlas 2009)


data from WOA2009



The ocean


20 21 22 23 24 25 26 27 28 29 30Potential density [kg m−3]

0

500

1000

1500

2000

Dep

th [m

]

Mean potential density (World Ocean Atlas 2009)


mixing depends on vertical gradient

data from WOA2009


lecture 2: structure and composition of the atmosphere and ... · lecture 2: structure and...

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