Download Feedbacks and climate sensitivity

Feedbacks and climate sensitivity
Program on Climate Change,
Summer Institute.
Feedbacks are found in many forms:
Mechanical feedbacks used in water clocks in ancient Greece.
Float valve,
Greek Clepsydra (“water thief”)
Feedbacks are found in many forms:
A feedback in every bathroom….
Ballcock assembly
Feedbacks are found in many forms:
James Watt’s governor
“Science”
Holborn viaduct,
London
Feedbacks are found in many forms:
Centrifugal governors in windmills since 16th century.
Centrifugal governor,
Dutch Mill
“On governors” Maxwell, 1869
Feedback analysis
Formalized framework for the evaluation of interactions in
dynamical systems.
- introduced the concept of negative
feedback.
- got the idea on Lackawanna
ferry on his way to work.
Harold S. Black
(1898-1983)
- took nine years to get granted
a patent.
“Our patent application was treated in the
same manner one would a perpetual motion
machine” Black, H.S. IEEE Spectrum, 1977
Original notes scribbled
on NY Times
Feedback analysis
The language of feedbacks is ubiquitous in Earth Sciences
(Maxwell, 1863; Black, 1927; Cess, 1975; Charney et al., 1979; Hansen et al., 1984; Schlesinger
& Mitchell, 1985)
But the language is confused and abused…
U.S. National Research
Council report, 2003
- gets definitions of feedbacks wrong…
- Worth standardizing terminology
Feedback analysis
Definition of reference system is intrinsic to feedbacks
forcing, DR
reference
climate system
Climate sensitivity parameter defined by:
response, DT
DT0 = l0 DR
Feedback analysis
Adding a feedback
DR
reference
climate system
c1DT
So now
DT = l0(DR + c1DT )
DT
Feedback analysis
Adding a feedback
DR
reference
climate system
DT
c1DT
So now
DT = l0(DR + c1DT )
Additional radn forcing due
to system response to DR
Feedback analysis
Adding a feedback
reference
climate system
DR
c1DT
So now
DT = l0(DR + c1DT )
Rearrange for DT

l 0DR
DT 
1 c1l 0
DT
Feedback analysis
Technobabble
Feedback factor: f = c1l0
Gain 
(f  to fraction of output
fed back into input)
response with feedback
DT

response without feedback DT0
From before
And since

l 0DR
DT0
DT 

1 c1l 0 1 f
DT  GDT0:
1
G
(1 f)
(Gain is proportion by which
system has gained)
Feedback analysis
The gain curve
Range of possibilities:
- < f < 0:
0 < f < 1:
f > 1:
G < 1  response damped  NEGATIVE fdbk.
G > 1  response amplified  POSITIVE fdbk.
G undef.  Planet explodes…
Aspects of feedbacks I.
The compounding effect of multiple feedbacks
DR
reference
climate system
DT
c1DT
c2DT
Now have
DT = l0(DR + c1DT + c2DT)
The effect of one feedback is
influenced by the strength of
the others..
(two nudges)
DT
G

DT0
1
N
1  fi
i1
Aspects of feedbacks II.
Comparing different feedbacks
DR
reference
climate
system
DT
c1DT
c2DT
The relative importance of two different feedbacks must be
evaluated relative to the same reference system.
There is a danger is comparing separate studies where only one
piece of physics has been isolated.
Aspects of feedbacks III.
How does uncertainty in feedbacks translate into uncertainty in
the system response?
∆T = ∆T0
DT for 2 x CO2 (oC)
1-f
Aspects of feedbacks III.
How does uncertainty in feedbacks translate into uncertainty in
the system response?
∆T = ∆T0
DT for 2 x CO2 (oC)
1-f
f
Aspects of feedbacks III.
How does uncertainty in feedbacks translate into uncertainty in
the system response?
∆T = ∆T0
DT for 2 x CO2 (oC)
1-f
T
f
Aspects of feedbacks III.
How does uncertainty in feedbacks translate into uncertainty in
the system response?
∆T = ∆T0
DT for 2 x CO2 (oC)
1-f
T
f
f
Aspects of feedbacks III.
How does uncertainty in feedbacks translate into uncertainty in
the system response?
∆T = ∆T0
1-f
DT for 2 x CO2 (oC)
T
T
f
f
Systems of strong positive feedbacks inherently less predictable
Aspects of feedbacks IV.
The relationship between feedbacks and response time
climate model response
(mean & 95% bounds)
to step function in forcing
Cl0

1  f i
i
Positive feedback systems have inherently long response times

Aspects of feedbacks V.
Diagnosing feedbacks from models and observations
For ith climate variable:
So feedback factors:


ciDT  R
j, ji
R  di

DT

i  j, ji dT
DR 
Di
fi  l0
 
Di  j, ji DT
i - can be a lumped property (like clouds, sea ice, etc.),

- or individual model
parameter (like entrainment coefficient)
- can also calculate spatial variations in fi if desired.
Aspects of feedbacks V.
Diagnosing feedbacks from models and observations
Springtime snow albedo feedback
(Fernandes et al., 2009)
Feedback factor of ice albedo
on sea-ice thickness (Bitz, 2008)
Aspects of feedbacks VI.
The variable of interest matters…
The same physical process can be a positive or negative feedback
depending on the variable of interest.
e.g., dynamic sea-ice is
- a positive feedback on surface air temperatures
- a negative feedback on mixed layer temperature
Strengths of feedback analysis.
Good points:
• Feedback analysis powerful representation of system dynamics
-system will try to adjust via most negative feedback.
• Can be used to propagate how uncertainty in one process
controls uncertainty in system response.
• Puts different mechanisms in the same non-dimensional
language.
e.g., Gaia is just a number….
fGaia ~ -0.65 (which is pretty absurd)
Issues with feedback analysis.
Not always a useful technique...
- Is the system linear enough that is makes sense to isolate the
individual feedbacks? (The Humpty Dumpty test)
- Is the reference system and variable of interest clear when
comparing different feedbacks?
- Feedback analysis can get blurry when physics has different
timescales (what’s a forcing, and what’s a feedback?)
Climate sensitivity.
A benchmark of climate change.
An envelope of uncertainty.
1,200,000+ integrations,
75,000,000+ yrs model time(!);
Eqm. response of global,
annual mean sfc. T to 2 x
CO2.
6,000 model runs, perturbed
physics.
Slab ocean, Q-flux
12 model params. varied
What governs the shape of this distribution:
a) in observations?
b) in models?
Climate sensitivity.
Estimates from observations.
Global energy budget:
Rf
forcing


F

= storage +
(ocean)
l DT
1
atmospheric
response
In principle, get Rf, F, DT from observations, solve for l, then:
DT2xCO 2  l Rf 2xCO 2
Climate sensitivity.
DT
l
Rf  F
Estimates from modern observations.
IPCC 2007 (mainly, plus a bit from Kyle)

Forcing change
Temperature change
DT  0.76  0.1o C (1 )

Climate sensitivity.
DT
l
Rf  F
Estimates from modern observations.
IPCC 2007 (mainly, plus a bit from Kyle)

Forcing change
Temperature change
Rf  F  0.9  0.56Wm2 (1 )
DT  0.76  0.1o C (1 )


Climate sensitivity.
DT
l
Rf  F
Estimates from modern observations.
DT  0.76  0.1o C (1 )

 


Rf  F  0.9  0.56Wm2 (1 )

Climate sensitivity.
Estimates from last glacial maximum observations.
DT  5.0  1.0o C (1 )




Rf  6.5  1.5Wm2 (1 )

DT
l
Rf  F
Hansen et al.1984
n.b. F is assumed zero
(not necessarily true)
Climate sensitivity.
DT 
Estimates from models.
l0Rf
1  f i
Individual feedbacks
uncorrelated among
models, so can be
simply combined:

Soden & Held (2006):
f  0.62;  f  0.13

Colman (2003):
f  0.70;  f  0.14

• How does this uncertainty in physics translate to uncertainty in
climate sensitivity?
Climate sensitivity.
DT 
Estimates from models.

for:
f  0.65
 f  0.14

l0Rf
1  f i
Climate sensitivity.
DT 
Estimates from models.

for:
f  0.65
 f  0.14

l0Rf
1  f i
Climate sensitivity.
DT 
Estimates from models.

• GCMs produce climate sensitivity consistent with the
compounding effect of essentially-linear feedbacks.
l0Rf
1  f i
Climate sensitivity.
An aside: nonlinearity of feedbacks
From basic analysis:
dR
DR 
DT  O(DT2 )
dT
But can take
quadratic terms…
dR
1 d2R 2
3
DR 
DT 
DT

O(DT
)
2
dT
2 dT

giving…

1
G
DT df
1 f 
2 dT
Taking ~12 different
 studies:
0.04K
1
df

 0.04K 1
dT
Climate sensitivity.
An aside: nonlinearity of feedbacks
So not a big deal…..
Climate sensitivity.
Models and observations.
• All look pretty similar.
• How to do better?
Climate sensitivity.
How to do better?
1. Combine different estimates?
Very hard to establish the degree of independence of individual
estimates.
2. Use other observations?
(e.g., NH vs. SH; pole-to-eq. DT; seasonality, trop. water vapor)
Structural errors among models highly uncertain (see Knutti et al, 2010).
3. Transient climate response?
Clim. Sens. is an equilibrium property, short observations only
have limited resolving power.
Fortunately...
Feedbacks don’t exist,
and
climate sensitivity doesn’t matter!
Feedbacks don’t exist.
reference
climate system
DR
DT
c1DT
c2DT
They are just a Taylor series in disguise
DRf 
DT
l0
 c1DT  c 2DT  c 3DT  c 4DT  K
reference system

(Thanks Kyle and Aaron)
Feedbacks don’t exist.
reference
climate system
DR
DT
c1DT
c2DT
They are just a Taylor series in disguise

DRf 
DT
l0
 c1DT  c 2DT  c 3DT  c 4DT  K
1

DRf    c1 DT  c2DT  c3DT  c 4DT K
 l0

why not this?

(Thanks Kyle and Aaron)
Feedbacks don’t exist.
reference
climate system
DR
DT
c1DT
c2DT
They are just a Taylor series in disguise.
DRf 
DT
l0
 c1DT  c 2DT  c 3DT  c 4DT  K
1

DRf    c1 DT  c2DT  c3DT  c 4DT K
 l0


1

DRf    c1  c2 DT  c3DT  c 4DT K
 l0


or this??
• Feedbacks are entirely in the eye of the beholder!

(Thanks Kyle and Aaron)
Climate sensitivity doesn’t matter.
Constraining climate sensitivity is not terribly relevant for
projecting climate change…
(Allen and Frame, 2007)
Stabilization target
of 450 ppm at 2100
High end sensitivities take a long, long time to be realized…
Climate sensitivity doesn’t matter.
Constraining climate sensitivity is not terribly relevant for
projecting climate change…
(Allen and Frame, 2007)
Concentration
target adjusted
at 2050.
Geoengineering = the human feedback.
Miscellany
Time dependent climate change:
The role of the ocean
• The ocean heat uptake acts as a (transient) negative feedback.