simple models for the h2o and co greenhouse...
TRANSCRIPT
SimplemodelsfortheH2OandCO2greenhouseeffects
withapplications
NadirJeevanjeeHessFellow
PrincetonUniversity
w/StephanFueglistaler (Princeton),JacobT.Seeley (Berkeley),DavidPaynter(GFDL),andDavidRomps(Berkeley)
OLR
Oceansurface
Space
Atmosphere
Sunlight
BoundaryLayerCo
nvectio
nEvap
Whatis`the’greenhouseeffect?
Qnet =LP(W/m2)
Quantity Value Simple Model Insight
2XCO2forcing 4 W/m2 ?? ??
Atmosphericradiativecooling
2K/day ?? ??
Mean precipitationchange
2-3W/m2/K(2-3%/K)
?? ??
Agenda:aspectsofthegreenhouseeffect
ToolsLine-by-line(LBL)radiationmodel
• Accurateandcomprehensiveinfra-redradiativetransfercalculationusingdetailedmolecularspectroscopy
• Calculatesopticaldepthsτk andupwardanddownwardfluxesFkasfunctionofwavenumberk
Pencil+paperestimates• Someapproximationsrequired…
OLR
Oceansurface
Space
Atmosphere
Sunlight
BoundaryLayer
Evap
Convectio
n
IdealizedtropicalcolumnwithTs=300K,𝚪 =7k/kmRH=0.75CO2=280ppmv
z
UODA:theunitopticaldepthapproximation
Optical depth: ⌧(z) = |{z}abs. coe↵
(m
2/kg)
Z 1
z⇢vdz
0
| {z }(kg/m2
)
=Total e↵ective area
Actual area
z
Optical depth: ⌧(z) = |{z}abs. coe↵
(m
2/kg)
Z 1
z⇢vdz
0
| {z }(kg/m2
)
=Total e↵ective area
Actual area
⌧ < 1 optically thin
⌧ ⇡ 1 just right
⌧ > 1 optically thick
⌧ < 1 optically thin
⌧ ⇡ 1 just right
⌧ > 1 optically thick
UODA:theunitopticaldepthapproximation
z
Optical depth: ⌧(z) = |{z}abs. coe↵
(m
2/kg)
Z 1
z⇢vdz
0
| {z }(kg/m2
)
=Total e↵ective area
Actual area
⌧ < 1 optically thin
⌧ ⇡ 1 just right
⌧ > 1 optically thick
UODA:theunitopticaldepthapproximationUODA:Emissiontospacecomesfromunitopticaldepth
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum
κ (m
2kg
)
k (cm−1)200 600 1000 140010
0060
020
0
log of optical depth τk
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Cooling−to−space (W m2 hPa cm−1)
Pres
sure
(hPa
)
−0.0015
−0.0010
−0.0005
0.0000
0.0005
0.0010
0.0015
k (cm−1)
AspectralviewofUODA
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum
κ (m
2kg
)
k (cm−1)200 600 1000 140010
0060
020
0
log of optical depth τk
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Cooling−to−space (W m2 hPa cm−1)
Pres
sure
(hPa
)
−0.0015
−0.0010
−0.0005
0.0000
0.0005
0.0010
0.0015
k (cm−1)
AspectralviewofUODA
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum
κ (m
2kg
)
k (cm−1)200 600 1000 140010
0060
020
0
log of optical depth τk
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Cooling−to−space (W m2 hPa cm−1)
Pres
sure
(hPa
)
−0.0015
−0.0010
−0.0005
0.0000
0.0005
0.0010
0.0015
k (cm−1)
AspectralviewofUODA
UseUODA tobuildsimplemodelforCO2forcing
Step1:Parameterize absorption coeffsandopticaldepth
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
500 600 700 8001000
200
5010
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
k0
κ0
500 600 700 8001000
200
5010
ln τk, Theory
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
(k) = 0 exp
✓� |k � k0|
lk
◆
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
500 600 700 8001000
200
5010
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
k0
κ0
500 600 700 8001000
200
5010
ln τk, Theory
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
Step1:Parameterize absorption coeffsandopticaldepth
(k) = 0 exp
✓� |k � k0|
lk
◆⌧k = (k)
qp2
2gpref
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
500 600 700 8001000
200
5010
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
k0
κ0
500 600 700 8001000
200
5010
ln τk, Theory
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
500 600 700 8001000
200
5010
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
500 600 700 8001e−0
51e−0
11e
+03
Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
k0
κ0
500 600 700 8001000
200
5010
ln τk, Theory
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)
⌧k(p) = (k)qp2
2gps
=) p1(k) =
r2gpsq0| {z }
p0(q)
exp
✓|k � k0|
2lk
◆
Step2.Find𝜏=1emissionlevels,denoted p1(k):
⌧k(p) = (k)qp2
2gps
=) p1(k) =
r2gpsq0| {z }
p0(q)
exp
✓|k � k0|
2lk
◆
Step2.Find𝜏=1emissionlevels,denoted p1(k):
600 650 700 7501000
200
5020
CO2 emission levels
k ( cm−1 )
p 1 (hPa)
CO2 (ppmv)280
⌧k(p) = (k)qp2
2gps
=) p1(k) =
r2gpsq0| {z }
p0(q)
exp
✓|k � k0|
2lk
◆
Step2.Find𝜏=1emissionlevels,denoted p1(k):
600 650 700 7501000
200
5020
CO2 emission levels
k ( cm−1 )
p 1 (hPa)
CO2 (ppmv)2801120
⌧k(p) = (k)qp2
2gps
=) p1(k) =
r2gpsq0| {z }
p0(q)
exp
✓|k � k0|
2lk
◆
Step2.Find𝜏=1emissionlevels,denoted p1(k):
600 650 700 7501000
200
5020
CO2 emission levels
k ( cm−1 )
p 1 (hPa)
∆k = lk ln4
CO2 (ppmv)2801120
Step3.ConstructapictureforCO2 forcing:
Negativestratosphericcontribution
Noforcingcontribution
Positivesurfacecontribution
CO2 forcinglogarithmic,andonlydependsonsurface-stratospheretemperaturecontrast!
F4⇥ = 2 lk ln 4| {z }
�k
2
64 ⇡B(k0
, Ts)| {z }surface
�⇡B(k0
, T (p0
))| {z }stratosphere
3
75
Step4.EstimateCO2 forcing(Wilson2012):600 650 700 75010
00200
5020
CO2 emission levels
k ( cm−1 )
p 1 (hPa)
∆k = lk ln4
CO2 (ppmv)2801120
ValidationofformulaF4⇥ = 2 lk ln 4| {z }
�k
2
64 ⇡B(k0
, Ts)| {z }surface
�⇡B(k0
, T (p0
))| {z }stratosphere
3
75
OLR
Oceansurface
Space
Atmosphere
Sunlight
BoundaryLayer
Evap
Convectio
n
VaryTsinidealizedtropicalcolumn
0 5 10 15
05
1015
CO2 Forcing
F4xLBL ( W m2 )
F 4xTheory
( W
m2 )
●●
●
●
●
●
●●
●
●
●
●
●
●
Ts (K)250260270280290300310
Caveats:• Clear-skyonly
(noclouds)• RH=0,CO2only
(noH2Ooverlap)• Idealizedatmosphere
(constantRHetc.)• Nostratospheric
adjustment
Back-of-the-envelope
F2⇥ ⇡ 2lk ln 2| {z }15 cm�1
[ ⇡B(k0, 288 K)| {z }0.4 W/m2/cm�1
� ⇡B(k0, 220 K)| {z }0.15 W/m2/cm�1
]
⇡ 3.7 W/m2
Back-of-the-envelope
F2⇥ ⇡ 2lk ln 2| {z }15 cm�1
[ ⇡B(k0, 288 K)| {z }0.4 W/m2/cm�1
� ⇡B(k0, 220 K)| {z }0.15 W/m2/cm�1
]
⇡ 3.7 W/m2
Back-of-the-envelope
F2⇥ ⇡ 2lk ln 2| {z }15 cm�1
[ ⇡B(k0, 288 K)| {z }0.4 W/m2/cm�1
� ⇡B(k0, 220 K)| {z }0.15 W/m2/cm�1
]
⇡ 3.7 W/m2
Quantity Value Simple Model Insight
2XCO2forcing 4 W/m2 2𝑙%ln2 𝐵% 𝑇+ − 𝐵% 𝑇-./0. Logscaling,Ts-Tstrattemp contrast
Atmosphericradiativecooling
2K/day ?? ??
Mean precipitationchange
2-3W/m2/K(2-3%/K)
?? ??
Agenda:aspectsofthegreenhouseeffect
Quantity Value Simple Model Insight
2XCO2forcing 4 W/m2 2𝑙%ln2 𝐵% 𝑇+ − 𝐵% 𝑇-./0. Logscaling,Ts-Tstrattemp contrast
Atmosphericradiativecooling
2K/day ?? ??
Mean precipitationchange
2-3W/m2/K(2-3%/K)
?? ??
Agenda:aspectsofthegreenhouseeffect
2K/dayremarkablyrobust
−50 0 501000
600
200
ECMWF radiative heating (K/day)
Latitude (deg)
Pres
sure
(hPa
)
−3
−2
−1
0
1
2
3
−6 −4 −2 0
1000
600
200
0
Radiative heating profiles
Heating (K/day)
Pres
sure
(hPa
) ECMWF
2K/dayremarkablyrobust
−50 0 501000
600
200
ECMWF radiative heating (K/day)
Latitude (deg)
Pres
sure
(hPa
)
−3
−2
−1
0
1
2
3
−6 −4 −2 0
1000
600
200
0
Radiative heating profiles
Heating (K/day)
Pres
sure
(hPa
) ECMWF
OLR
Oceansurface
Space
Atmosphere
Sunlight
BoundaryLayer
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Convectio
n
Canemulatewithsingle-columnLBL,H2Oonly,nocont.
2K/dayremarkablyrobust
−50 0 501000
600
200
ECMWF radiative heating (K/day)
Latitude (deg)
Pres
sure
(hPa
)
−3
−2
−1
0
1
2
3
−6 −4 −2 0
1000
600
200
0
Radiative heating profiles
Heating (K/day)
Pres
sure
(hPa
) ECMWFLBL
OLR
Oceansurface
Space
Atmosphere
Sunlight
BoundaryLayer
Evap
Convectio
n
Canemulatewithsingle-columnLBL,H2Oonly,nocont.
Thecooling-to-spaceapproximation
Hk =g
Cp@pFk| {z }Flux
div.
⇡ � g
Cp⇡B(k, T )| {z }
Planck
d⌧kdp|{z}
emissivity
gradient
e�⌧k|{z}trans-
missivity
200 600 1000 14001000
600
200
Radiative heating Hk (K day cm−1)
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)200 600 1000 140010
0060
020
0
Cooling−to−space (K day cm−1)
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
Thecooling-to-spaceapproximation
200 600 1000 14001000
600
200
Radiative heating Hk (K day cm−1)
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)200 600 1000 140010
0060
020
0
Cooling−to−space (K day cm−1)
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
Hk =g
Cp@pFk| {z }Flux
div.
⇡ � g
Cp⇡B(k, T )| {z }
Planck
d⌧kdp|{z}
emissivity
gradient
e�⌧k|{z}trans-
missivity
Thecooling-to-spaceapproximation
200 600 1000 14001000
600
200
Radiative heating Hk (K day cm−1)
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)200 600 1000 140010
0060
020
0
Cooling−to−space (K day cm−1)
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
Hk =g
Cp@pFk| {z }Flux
div.
⇡ � g
Cp⇡B(k, T )| {z }
Planck
d⌧kdp|{z}
emissivity
gradient
e�⌧k|{z}trans-
missivity
SimplemodelforH2Ocooling
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, LBL ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, TheoryPr
essu
re (h
Pa)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, Theory ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
(k) ⌘ rot
exp
✓�k � k
rot
lrot
◆
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, LBL ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, TheoryPr
essu
re (h
Pa)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, Theory ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
SimplemodelforH2Ocooling
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, LBL ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, TheoryPr
essu
re (h
Pa)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, Theory ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
(k) ⌘ rot
exp
✓�k � k
rot
lrot
◆⌧k = (k)
p
prefWVP0 exp
✓� L
RvT
◆
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, LBL ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, TheoryPr
essu
re (h
Pa)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, Theory ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
SimplemodelforH2Ocooling
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, LBL ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, TheoryPr
essu
re (h
Pa)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, Theory ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
(k) ⌘ rot
exp
✓�k � k
rot
lrot
◆⌧k = (k)
p
prefWVP0 exp
✓� L
RvT
◆Hk ⇡ � g
Cp⇡B(k, T )
d⌧kdp
e�⌧k
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, LBL ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, TheoryPr
essu
re (h
Pa)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, Theory ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
Simplemodel `emulates’comprehensivemodel (Jeevanjeeetal.2017,JAMES)
Canwedothespectral integral?
H ⇡ g
Cp
Z⇡B(k, T )
d⌧kdp
e�⌧kdk (K/day)
⇡ g
Cp
Z⇡B(k, T )
d ln ⌧kdp| {z }�/p
⌧ke�⌧k
| {z }�(⌧k�1)
dk
d⌧k|{z}lk
d⌧k
⇡ g
Cp⇡B(k1, T )
�
plk
Canwedothespectral integral?
H ⇡ g
Cp
Z⇡B(k, T )
d⌧kdp
e�⌧kdk (K/day)
⇡ g
Cp
Z⇡B(k, T )
d ln ⌧kdp| {z }�/p
⌧ke�⌧k
| {z }�(⌧k�1)
dk
d⌧k|{z}lk
d⌧k
⇡ g
Cp⇡B(k1, T )
�
plk
Canwedothespectral integral?
H ⇡ g
Cp
Z⇡B(k, T )
d⌧kdp
e�⌧kdk (K/day)
⇡ g
Cp
Z⇡B(k, T )
d ln ⌧kdp| {z }�/p
⌧ke�⌧k
| {z }�(⌧k�1)
dk
d⌧k|{z}lk
d⌧k
⇡ g
Cp⇡B(k1, T )
�
plk
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, LBL
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, LBL
Pres
sure
(hPa
)
−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, LBL ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
200 600 1000 14001e−0
41e
+00
1e+0
4 Absorption spectrum, fit
k (cm−1)
κ (m
2kg
)
200 600 1000 14001000
600
200
ln τk, Theory
Pres
sure
(hPa
)−20
−10
0
10
20
k (cm−1)200 600 1000 140010
0060
020
0
Hk, Theory ( K day cm−1 )
Pres
sure
(hPa
)
−0.010
−0.005
0.000
0.005
0.010
k (cm−1)
k1
PlanckEmissivitygradientSpectralwidth
H ⇡ � g
Cp⇡B(k1, T )
�
plkTestformula
−50 0 501000
600
200
ECMWF radiative heating (K/day)
Latitude (deg)
Pres
sure
(hPa
)
−3
−2
−1
0
1
2
3
−6 −4 −2 010
0060
020
00
Radiative heating profiles
Heating (K/day)
Pres
sure
(hPa
) ECMWFLBL
H ⇡ � g
Cp⇡B(k1, T )
�
plkTestformula
−50 0 501000
600
200
ECMWF radiative heating (K/day)
Latitude (deg)
Pres
sure
(hPa
)
−3
−2
−1
0
1
2
3
−6 −4 −2 010
0060
020
00
Radiative heating profiles
Heating (K/day)
Pres
sure
(hPa
) ECMWFLBLTheory
Back-of-the-envelope
H ⇡ �✓
g
Cp
◆(⇡B(k1, T ) lk)
✓�H2O
p
◆
⇡ �✓10�4 K/s
W/m2/hPa
◆(20 W/m2)
✓1
100 hPa
◆
= � 2⇥ 10�5 K/s
⇡ � 2 K/day .
Back-of-the-envelope
H ⇡ �✓
g
Cp
◆(⇡B(k1, T ) lk)
✓�H2O
p
◆
⇡ �✓10�4 K/s
W/m2/hPa
◆(20 W/m2)
✓1
100 hPa
◆
= � 2⇥ 10�5 K/s
⇡ � 2 K/day .
Back-of-the-envelope
H ⇡ �✓
g
Cp
◆(⇡B(k1, T ) lk)
✓�H2O
p
◆
⇡ �✓10�4 K/s
W/m2/hPa
◆(20 W/m2)
✓1
100 hPa
◆
= � 2⇥ 10�5 K/s
⇡ � 2 K/day .
Back-of-the-envelope
H ⇡ �✓
g
Cp
◆(⇡B(k1, T ) lk)
✓�H2O
p
◆
⇡ �✓10�4 K/s
W/m2/hPa
◆(20 W/m2)
✓1
100 hPa
◆
= � 2⇥ 10�5 K/s
⇡ � 2 K/day .
Quantity Value Simple Model Insight
2XCO2forcing 4 W/m2 2𝑙1ln2[𝐵% 𝑇+ − 𝐵% 𝑇-./0. ] Logscaling,Ts-Tstrattemp contrast
Atmosphericradiativecooling
2K/day −𝑔𝐶6𝜋𝐵 𝑘9 𝑇 , 𝑇
𝛽𝑝𝑙/=.
(Planck) x(emissivity)x
(spectralwidth)
Mean precipitationchange
2-3W/m2/K(2-3%/K)
?? ??
Agenda:aspectsofthegreenhouseeffect
Quantity Value Simple Model Insight
2XCO2forcing 4 W/m2 2𝑙1ln2[𝐵% 𝑇+ − 𝐵% 𝑇-./0. ] Logscaling,Ts-Tstrattemp contrast
Atmosphericradiativecooling
2K/day −𝑔𝐶6𝜋𝐵 𝑘9 𝑇 , 𝑇
𝛽𝑝𝑙/=.
(Planck) x(emissivity)x
(spectralwidth)
Mean precipitationchange
2-3W/m2/K(2-3%/K)
?? ??
Agenda:aspectsofthegreenhouseeffect
OLR
Oceansurface
Space
Atmosphere
Sunlight
BoundaryLayerEvap
Convectio
n
Whatis`the’greenhouseeffect?
Qnet =LP(W/m2)
Modelsrobustlypredict>?@1ABC>DE
≈ 2%KI9 .Why?
Toanswerthis,notethatopticaldepth𝜏% = 𝜅 𝑘 6
6LBMWVPQexp(−
VWXD
)isdominatedbyT-dependence!
Butheatingrate𝐻 = [\]𝜕6𝐹 isaflux-divergence inp-coordinates.
WhatifwechangetoT-coordsanduseCTSapprox?
𝜕D𝐹 ≈ −𝜋𝐵 𝑘9(𝑇),𝑇𝑑ln𝜏%a𝑑𝑇 𝑙%
ThisdependsalmostentirelyonTalone!
!"# isTs-invariant
−5 −4 −3 −2 −1 0
300
260
220
LBL
∂TF (W m2 K)
Tem
pera
ture
(K)
−5 −4 −3 −2 −1 030
026
022
0
Theory
∂TF (W m2 K)
Tem
pera
ture
(K)
OLR
Oceansurface
Space
AtmosphereSunligh
t
BoundaryLayer
Evap
Convection
single-columnLBL,H2Oonly,nocont.
!"# isTs-invariant
−5 −4 −3 −2 −1 0
300
260
220
LBL
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270
−5 −4 −3 −2 −1 030
026
022
0
Theory
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270
OLR
Oceansurface
Space
AtmosphereSunligh
t
BoundaryLayer
Evap
Convection
single-columnLBL,H2Oonly,nocont.
!"# isTs-invariant
−5 −4 −3 −2 −1 0
300
260
220
LBL
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270280
−5 −4 −3 −2 −1 030
026
022
0
Theory
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270280
OLR
Oceansurface
Space
AtmosphereSunligh
t
BoundaryLayer
Evap
Convection
single-columnLBL,H2Oonly,nocont.
!"# isTs-invariant
−5 −4 −3 −2 −1 0
300
260
220
LBL
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270280290
−5 −4 −3 −2 −1 030
026
022
0
Theory
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270280290
OLR
Oceansurface
Space
AtmosphereSunligh
t
BoundaryLayer
Evap
Convection
single-columnLBL,H2Oonly,nocont.
!"# isTs-invariant
−5 −4 −3 −2 −1 0
300
260
220
LBL
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270280290300
−5 −4 −3 −2 −1 030
026
022
0
Theory
∂TF (W m2 K)
Tem
pera
ture
(K)
Ts (K)
270280290300
OLR
Oceansurface
Space
AtmosphereSunligh
t
BoundaryLayer
Evap
Convection
single-columnLBL,H2Oonly,nocont.
ASimplePicturefordQ/dTs
Q
(�@TF )(Ts)
Q
�Q�@TFTs
T
dQ
dTs⇡ (�@TF )(Ts) (W/m2/K)
�Ts
T
�@TF
�Ts
OLR
Oceansurface
Space
Atmosphere
Sunlight
BoundaryLayer
Evap
Convectio
nRadiative-convectiveequilibrium(RCE)
Qnet =LP(W/m2)
Model:DAM(Romps2008)MovieCredit:JacobT.SeeleySurfacecolors=low-levelair temp
Test formula,butinwhatvenue?
Limitedareacloud-resolvingmodel
Howdoesourformulado?
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
dQ
dTs⇡ (�@TF )(Ts)
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
●
●
●
●● Qnet
Howdoesourformulado?
dQ
dTs⇡ (�@TF )(Ts)
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
●
●
●
●● Qnet
P
Howdoesourformulado?
dQ
dTs⇡ (�@TF )(Ts)
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
●
●
●
●● Qnet
PTheory
Howdoesourformulado?
dQ
dTs⇡ (�@TF )(Ts)
1
P
dP
dTs(300 K) ⇡ 1
Q
dQ
dTs(300 K)
⇡ (�@TF )(300 K)
Q(300 K)
=3 W/m2/K
100 W/m2
= 3% K�1
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
●
●
●
●● Qnet
PTheory
Howdoesourformulado?
dQ
dTs⇡ (�@TF )(Ts)
1
P
dP
dTs(300 K) ⇡ 1
Q
dQ
dTs(300 K)
⇡ (�@TF )(300 K)
Q(300 K)
=3 W/m2/K
100 W/m2
= 3% K�1
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
●
●
●
●● Qnet
PTheory
Howdoesourformulado?
dQ
dTs⇡ (�@TF )(Ts)
1
P
dP
dTs(300 K) ⇡ 1
Q
dQ
dTs(300 K)
⇡ (�@TF )(300 K)
Q(300 K)
=3 W/m2/K
100 W/m2
= 3% K�1
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
●
●
●
●● Qnet
PTheory
Howdoesourformulado?
dQ
dTs⇡ (�@TF )(Ts)
1
P
dP
dTs(300 K) ⇡ 1
Q
dQ
dTs(300 K)
⇡ (�@TF )(300 K)
Q(300 K)
=3 W/m2/K
100 W/m2
= 3% K�1
280 290 300 310
4060
8010
012
014
0
Net cooling and precip vs. Ts
Ts (K)
Qne
t, P
(
Wm
2 )
●
●
●
●● Qnet
PTheory
Howdoesourformulado?
dQ
dTs⇡ (�@TF )(Ts)
1
P
dP
dTs(300 K) ⇡ 1
Q
dQ
dTs(300 K)
⇡ (�@TF )(300 K)
Q(300 K)
=3 W/m2/K
100 W/m2
= 3% K�1
Intuitionfor2-3%perK?
0 1 2 3 4 5
300
260
220
180
Flux Divergence
−∂TF ( W m2 K )
Tem
pera
ture
(K)
Q
�@TF ⇠ (T � Ttp)� , � ⇡ 1
=) Q(Ts) ⇠ (Ts � Ttp)�+1
=) d lnQ
dTs=
� + 1
Ts � Ttp⇡ 2% K�1 !
Ttp
Intuitionfor2-3%perK?
0 1 2 3 4 5
300
260
220
180
Flux Divergence
−∂TF ( W m2 K )
Tem
pera
ture
(K)
Q
�@TF ⇠ (T � Ttp)� , � ⇡ 1
=) Q(Ts) ⇠ (Ts � Ttp)�+1
=) d lnQ
dTs=
� + 1
Ts � Ttp⇡ 2% K�1 !
Ttp
�@TF ⇠ (T � Ttp)� , � ⇡ 1
=) Q(Ts) ⇠ (Ts � Ttp)�+1
=) d lnQ
dTs=
� + 1
Ts � Ttp⇡ 2% K�1 !
Intuitionfor2-3%perK?
0 1 2 3 4 5
300
260
220
180
Flux Divergence
−∂TF ( W m2 K )
Tem
pera
ture
(K)
Q
�@TF ⇠ (T � Ttp)� , � ⇡ 1
=) Q(Ts) ⇠ (Ts � Ttp)�+1
=) d lnQ
dTs=
� + 1
Ts � Ttp⇡ 2% K�1 !
Ttp
�@TF ⇠ (T � Ttp)� , � ⇡ 1
=) Q(Ts) ⇠ (Ts � Ttp)�+1
=) d lnQ
dTs=
� + 1
Ts � Ttp⇡ 2% K�1 !
Keyfact:1Kincrease inTs is1%increase inatmosphericdepthTs-Ttp
Quantity Value Simple Model Insight
2XCO2forcing 4 W/m2 2𝑙1ln2[𝐵% 𝑇+ − 𝐵% 𝑇-./0. ] Logscaling,Ts-Tstrattemp contrast
Atmosphericradiativecooling
2K/day −𝑔𝐶6𝜋𝐵 𝑘9 𝑇 , 𝑇
𝛽𝑝𝑙/=.
(Planck) x(emissivity)x
(spectralwidth)
Mean precipitationchange
2-3W/m2/K(2-3%/K)
?? ??
Agenda:aspectsofthegreenhouseeffect
Quantity Value Simple Model Insight
2XCO2forcing 4 W/m2 2𝑙1ln2[𝐵% 𝑇+ − 𝐵% 𝑇-./0. ] Logscaling,Ts-Tstrattemp contrast
Atmosphericradiativecooling
2K/day −𝑔𝐶6𝜋𝐵 𝑘9 𝑇 , 𝑇
𝛽𝑝𝑙/=.
(Planck) x(emissivity)x
(spectralwidth)
Mean precipitationchange
2-3W/m2/K(2-3%/K)
(−𝜕D𝐹@b.) cDEJeevanjee andRompsPNAS2018
Troposphericdeepening
Agenda:aspectsofthegreenhouseeffect
Thankyou!
ValidationforCO2only
50 150 250 350
−50
050
F4X , CO2 only, LBL
Longitude (deg)
Latit
ude
(deg
)
0
5
10
15Global mean = 7.7 W m2
50 150 250 350
−50
050
F4X , CO2 only, Theory
Longitude (deg)
Latit
ude
(deg
)
0
5
10
15Global mean = 7.6 W m2
0 5 10 15
−50
050
F4X , CO2 only
F4X (W m2)La
titud
e (d
eg)
LBLTheory
F4⇥ = 2 lk ln 4| {z }
�k
2
64 ⇡B(k0
, Ts)| {z }surface
�⇡B(k0
, T (p0
))| {z }stratosphere
3
75
F4x variationsdeterminedbyTs variations
F4⇥ = 2 lk ln 4| {z }
�k
2
64 ⇡B(k0
, Ts)| {z }surface
�⇡B(k0
, T (p0
))| {z }stratosphere
3
75
50 150 250 350
−50
050
F4X , CO2 only, LBL
Longitude (deg)
Latit
ude
(deg
)
0
5
10
15W m2
50 150 250 350
−50
050
Surface Temperature
Longitude (deg)
Latit
ude
(deg
)
220240260280300320340
K
Futurework– H2Oeffects
50 150 250 350
−50
050
F4X , CO2 only
Longitude (deg)
Latit
ude
(deg
)
0
5
10
15Global mean = 7.7 W m2
50 150 250 350
−50
050
F4X , all gases
Longitude (deg)
Latit
ude
(deg
)
0
5
10
15Global mean = 5 W m2
0 5 10 15
−50
050
F4X
F4X (W m2)
Latit
ude
(deg
)
CO2 onlyall gases