Biospheric Theory
and Modelling
An earth system’s approach to the
sensitivity of the water cycle
Maik Renner and Axel Kleidon
Max-Planck-Institut für Biogeochemie, Jena, Germany
26. October 2016
EGU-Leonardo conference on the hydrological cycle, Ourense
System (CERES, Wielicki et al. 1996) and the Solar
Radiation and Climate Experiment (SORCE, Anderson and
Cahalan 2005). These allow the determination of the top of
available from ground-based radiation networks (Sect. 2).
We use these observations to assess the radiation budgets as
simulated in the latest modeling efforts performed within
Fig. 1 Schematic diagram of the global mean energy balance of the
Earth. Numbers indicate best estimates for the magnitudes of the
globally averaged energy balance components together with their
uncertainty ranges, representing present day climate conditions at the
et al 2013,
Clim.
Dyn
beginning of the twentyWild
first century.
Estimates
and uncertainty
Renner and Kleidon EGU-Leonardo 2016
ranges based on discussion in Sect. 5. Units Wm-2
Water cycle ~ radiation and convection
2
Systems’ perspective on earth
Global climate
model
dynamic state
equations
sub-grid
parameterisations
natural system
processes
interacting at
multiple time scales
3
Renner and Kleidon EGU-Leonardo 2016
Systems’ perspective on earth
Global climate
model
dynamic state
equations
sub-grid
parameterisations
natural system
processes
interacting at
multiple time scales
Perfection is achieved, not when there is nothing more
to add, but when there is nothing left to take away.
Antoine de Saint-Exupery
Can we formulate a simple earth system model which
captures the most important (thermo)dynamics to predict the
response to radiative changes?
3
Renner and Kleidon EGU-Leonardo 2016
A simple climate model
energy balances as starting points
energy balances:
Ta
Rs
Rs
Rs:
R l:
H:
λE:
heat
engine
Rs
Rl
H λE
heat
E=0
absorbed solar radiation
net emission of terrestrial radiation
sensible heat flux
latent heat flux
given: absorbed solar radiation Rs
(= 240 W m-2) and surface
temperature Ts (= 288 K)
Ts
radiation
Rl H
4
Ta = 0
unknown: partitioning between
Rl and H + λE?
motion
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Renner and Kleidon EGU-Leonardo 2016
Atmospheric heat engine
thermodynamic limit on convective motion
first law: energy budget
Ta
0 = Jin
Jout
heat
engine
Rs
Rl
Jout
G
second law: entropy budget
G power to
generate
motion
Jin
Jout
Ta
best case:
Jin
Ts
Jout
0
Ta
= Jin
Ts
Ts
radiation
heat
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
5
Renner and Kleidon EGU-Leonardo 2016
Atmospheric heat engine
thermodynamic limit on convective motion
first law: energy budget
Ta
0 = Jin
Jout
heat
engine
Rs
Rl
G power to
generate
motion
Jin
heat
G
second law: entropy budget
Ts
radiation
Jout
Jout
Ta
best case:
Jin
Ts
Jout
0
Ta
= Jin
Ts
“Carnot” limit for G:
G = Jin
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
5
Ts
Ta
Ts
Renner and Kleidon EGU-Leonardo 2016
A simple climate model
exchange of terrestrial radiation
assume blackbody emission
for surface and atmosphere:
Ta
Rl,s = Ts4
Rl,a =
heat
engine
Rs
Rl
linearize emission:
T 4 ⇡ R0 + kr (T
H λE
heat
T0 )
results in simple expression for net
longwave radiative exchange:
Ts
radiation
4
Ta
Rl = Rl,s Rl,a
= kr (Ts Ta )
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
6
Renner and Kleidon EGU-Leonardo 2016
A simple climate model
parameterization of heat fluxes
convective heat fluxes depend on a
rate of mass exchange, ρw:
Ta
H = cp ⇢w(Ts
heat
engine
Rs
Rl
E = ⇢w(qs
convective
mass
exchange
s
Ts
radiation
heat
E = cp ⇢w (Ts
s
γ:
E= H
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
qa )
assume saturation for surface
and atmosphere and linearize
saturation vapor pressure curve
with slope s
ρw
H λE
Ta )
7
Ta )
psychrometric
constant
Renner and Kleidon EGU-Leonardo 2016
Carnot limit for generating convection
“Carnot” limit for G:
G=H·
Ta
heat
engine
Rs
Rl
Ts
Ta
Ts
use surface energy balance
to express ∆T:
G
power to
generate
motion
Ts
Ta =
Rs
H
kr
E
H λE
Ts
radiation
heat
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
8
Renner and Kleidon EGU-Leonardo 2016
Carnot limit for generating convection
“Carnot” limit for G:
G=H·
Ta
heat
engine
Rs
Rl
Ts
Ta
Ts
use surface energy balance
to express ∆T:
G
power to
generate
motion
Ts
Ta =
Rs
H
kr
E
maximize power G:
H λE
Ts
radiation
heat
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
8
Renner and Kleidon EGU-Leonardo 2016
Carnot limit for generating convection
“Carnot” limit for G:
G=H·
Ta
heat
engine
Rl
G
power to
generate
motion
Ts
Ta =
heat
Ts
Rs
H
kr
E
maximize power G:
H λE
Ts
radiation
Ta
use surface energy balance
to express ∆T:
power G
Rs
Ts
∆T
G
motion
convective heat flux
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
8
Renner and Kleidon EGU-Leonardo 2016
A simple climate model
flux partitioning at maximum convective power
max. power limit predicts equal
partitioning among radiative and
turbulent fluxes:
Ta
heat
engine
Rs
Rl
G
power to
generate
motion
H λE
Ts
radiation
heat
Rl,opt =
H=
s+
s
E=
s+
Rs
2
Rs
2
Rs
2
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
9
Renner and Kleidon EGU-Leonardo 2016
A simple climate model
flux partitioning at maximum convective power
max. power limit predicts equal
partitioning among radiative and
turbulent fluxes:
Ta
heat
engine
Rs
Rl
G
power to
generate
motion
H λE
Ts
radiation
heat
H=
s+
s
E=
s+
consistent with “equilibrium evaporation”
rate of Schmidt (1909) and Slayter &
McIlroy (1961), Priestley and Taylor (1971)
motion
Kleidon and Renner (2013) Hydrol. Earth Syst. Sci.
Rl,opt =
Rs
2
Rs
2
Rs
2
9
Renner and Kleidon EGU-Leonardo 2016
A simple climate model
surface energy partitioning on land
(with added water balance constraint)
Latent heat flux
latent heat flux
:1
1
100
150
climatological means
λE
0
50
:1
1
modelled
LE [Wm−2]
(W m-2)
power
max.
250
200
150
0° ≤ latitude ≤ 15°
15° < latitude ≤ 38°
38° < latitude ≤ 66°
66° < latitude ≤ 90°
50
100
ERA−Interim data
H + LE = Rs 2
0
turbulent heat fluxes
-2)W/m2
ERA Interim,
+ LE,
(WH m
Radiative and turbulent partitioning, ERA−Interim
0
50
100
150
200
250
0
absorbed
absorbed solar solar
radiation, radiation
SRB, W/m2
(W m-2)
Kleidon, Renner, Porada (2014) Hydrol. Earth Syst. Sci.
50
100
150
ERA-Interim
m-2)
ERA−Interim, LE(W
[Wm−2]
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Renner and Kleidon EGU-Leonardo 2016
1.0
Maximum Power
ERA−Interim
0.2
0.6
dRlu dRin
Max
Rln = Rsn /2
= Rlu (Ts )
imu
mp
owe
r
Rld
@Rlu /@Rld = 1
@Rlu /@Rsn = 1/2
dRn dRin
−0.2
Sensitivity to total incoming radiation Rin
Sensitivity to type of radiative forcing
0
longwave change
dominates
Renner, Dhara and Kleidon, in prep.
0.5
1
shortwave change
dominates
∆Rsn ∆Rin
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Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
Evaporation rate:
s Rs
+s 2
Eopt =
Kleidon and Renner (2013) ESD
Kleidon, Kravitz, Renner (2015) GRL
12
Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
Evaporation rate:
Relative sensitivity:
s Rs
Eopt =
+s 2
1
1 @E ds
1 @E
E=
Ts +
Rs
E
E @s dTs
E @Rs
Kleidon and Renner (2013) ESD
Kleidon, Kravitz, Renner (2015) GRL
12
Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
Evaporation rate:
Relative sensitivity:
s Rs
Eopt =
+s 2
1
1 @E ds
1 @E
E=
Ts +
Rs
E
E @s dTs
E @Rs
≈ 2.2 % K-1
≈ 1 % K-1
greenhouseinduced
warming:
2.2 % K-1
solar-induced
warming:
3.2 % K-1
Kleidon and Renner (2013) ESD
Kleidon, Kravitz, Renner (2015) GRL
12
Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
s Rs
Eopt =
+s 2
1
1 @E ds
1 @E
E=
Ts +
Rs
E
E @s dTs
E @Rs
Evaporation rate:
Relative sensitivity:
15
∆P/P (%)
10
Climate models
4xCO2
5
≈ 2.2 % K-1
≈ 1 % K-1
greenhouseinduced
warming:
2.2 % K-1
solar-induced
warming:
3.2 % K-1
Today
0
Climate
models
4*CO2 - ∆Rs
−5
−10
−2
−1
0
model sensitivity from
Tilmes et al. (2013) JGR
1
2
3
4
5
6
Kleidon and Renner (2013) ESD
Kleidon, Kravitz, Renner (2015) GRL
∆Ts (K)
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Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
s Rs
Eopt =
+s 2
1
1 @E ds
1 @E
E=
Ts +
Rs
E
E @s dTs
E @Rs
Evaporation rate:
Relative sensitivity:
15
4xCO2
∆P/P (%)
10
Climate models
4xCO2
5
+5 K
Today
0
≈ 2.2 % K-1
≈ 1 % K-1
greenhouseinduced
warming:
2.2 % K-1
solar-induced
warming:
3.2 % K-1
Climate
models
4*CO2 - ∆Rs
−5
−10
−2
−1
0
model sensitivity from
Tilmes et al. (2013) JGR
1
2
3
4
5
6
Kleidon and Renner (2013) ESD
Kleidon, Kravitz, Renner (2015) GRL
∆Ts (K)
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Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
s Rs
Eopt =
+s 2
1
1 @E ds
1 @E
E=
Ts +
Rs
E
E @s dTs
E @Rs
Evaporation rate:
Relative sensitivity:
15
-5 K
4xCO2
∆P/P (%)
10
Climate models
4xCO2
5
+5 K
Today
0
≈ 1 % K-1
greenhouseinduced
warming:
2.2 % K-1
solar-induced
warming:
3.2 % K-1
Climate
models
4*CO2 - ∆Rs
G
−5
≈ 2.2 % K-1
−10
−2
−1
0
model sensitivity from
Tilmes et al. (2013) JGR
1
2
3
4
5
6
Kleidon and Renner (2013) ESD
Kleidon, Kravitz, Renner (2015) GRL
∆Ts (K)
12
Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
Analogy: Increasing the temperature of a pot on a stove
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Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
Analogy: Increasing the temperature of a pot on a stove
Reduced
cooling
by lid
(“greenhouse”)
13
Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
Analogy: Increasing the temperature of a pot on a stove
Reduced
cooling
by lid
(“greenhouse”)
Increased
heating
by plate
(“solar”)
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Renner and Kleidon EGU-Leonardo 2016
Hydrologic Cycling and Surface Warming
Analogy: Increasing the temperature of a pot on a stove
Reduced
cooling
by lid
(“greenhouse”)
Increased
heating
by plate
(“solar”)
Solar geoengineering:
Compensate temperature increase by lid by reducing the heating
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Renner and Kleidon EGU-Leonardo 2016
Summary and Conclusions
Earth systems’ approach
•
•
atmosphere as a heat engine
•
•
thermodynamic optimality - state of maximum power
trade-off between temperature gradient and the
turbulent heat flux
allows first order predictions on earth system
Conclusion:
•
type of radiative change (SW <-> LW) is key to
predict response of temperature and water cycle
•
2.2% / K increase of water cycle by greenhouse
warming understood by saturation vapour pressure
constrained by surface energy balance
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Renner and Kleidon EGU-Leonardo 2016
References
Dhara, C., Renner, M., & Kleidon, A. (2016). Broad climatological variation of surface energy
balance partitioning across land and ocean predicted from the maximum power limit. Geophysical
Research Letters, 43(14), 2016GL070323. https://doi.org/10.1002/2016GL070323
Kleidon, A., Kravitz, B., & Renner, M. (2014). The hydrological sensitivity to global warming and
solar geoengineering derived from thermodynamic constraints. Geophysical Research Letters,
2014GL062589. https://doi.org/10.1002/2014GL062589
Kleidon, A., & Renner, M. (2013a). A simple explanation for the sensitivity of the hydrologic cycle to
surface temperature and solar radiation and its implications for global climate change. Earth
System Dynamics, 4(2), 455–465. https://doi.org/10.5194/esd-4-455-2013
Kleidon, A., & Renner, M. (2013b). Thermodynamic limits of hydrologic cycling within the Earth
system: concepts, estimates and implications. Hydrol. Earth Syst. Sci., 17(7), 2873–2892. https://
doi.org/10.5194/hess-17-2873-2013
Kleidon, A., Renner, M., & Porada, P. (2014). Estimates of the climatological land surface energy
and water balance derived from maximum convective power. Hydrology and Earth System
Sciences, 18(6), 2201–2218. https://doi.org/10.5194/hess-18-2201-2014
Tilmes, S., Fasullo, J., Lamarque, J.-F., Marsh, D. R., Mills, M., Alterskjær, K., … Watanabe, S.
(2013). The hydrological impact of geoengineering in the Geoengineering Model Intercomparison
Project (GeoMIP). Journal of Geophysical Research: Atmospheres, 118(19), 11,036-11,058. https://
doi.org/10.1002/jgrd.50868
Wild, M., Folini, D., Schär, C., Loeb, N., Dutton, E. G., & König-Langlo, G. (2013). The global
energy balance from a surface perspective. Climate Dynamics, 1–28. https://doi.org/10.1007/
s00382-012-1569-8
Thank you!
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Renner and Kleidon EGU-Leonardo 2016