A heiarchical framework for emergent constraints:
application to snow-albedo feedback and
chemistry-climate interaction
Prediction is difficult, especially about the future
--Niels Bohr
(Danish proverb)
Kevin W. Bowman1,2, Le Kuai2, Jeff Jewell1, Helen Worden3
Noelle Cressie4, Xi Qu3, Alex Hall3
1Jet
Propulsion Laboratory
California Institute of Technology
2Joint
Institute for Regional Earth System Science and Engineering
University of California, Los Angeles
3Department of
Atmospheric and Oceanic Sciences
University of California, Los Angeles
4National
Institute for Applied Statistics Research Australia (NIASRA)
University of Wollongong NSW 2522, Australia
© 2016 California Institute of Technology. Government sponsorship acknowledged
© 2012 California Institute of Technology. Government sponsorship acknowledged
A-Train: Benchmark for today—and tomorrow?
The A-train has given us an unprecedented view of the Earth System.
What does it tell us about the future?
Emergent constraints/correlations
One of the most basic principles in
science is that theories should be
testable—and falsifiable with
observations (Popper, 1934)
How can you falsify a prediction if
you’re already dead?
So-called “emergent” constraints are
an attempt to relate climate response
to present day climate variability
Hall and Qu, GRL (2006) and Qu and Hall (2014) showed that both the AR4 and AR5
climate ensemble model snow albedo feedback was linked to their seasonal cycle of
snow feedback strength, which in turn could be tested against the observed seasonal
cycle.
What is the probability that the feedback, e.g., SAF will be within a certain range, e.g.,
[-1,-0.5] %/K given observations?
How do uncertainties in present day, future response, and observations impact that
probability?
Emergent constraints
An emergent constraint are based upon two factors:
(1) A correlation between future and historic climate, which is
frequently determined through a climate model ensemble.
(2) Observations of historic climate.
What is the joint distribution of the future and the
present given observations of the present?
where
z t+t is the future state at t+τ
x t is the current state at t
y t are the observations at t
4
Predictability and Observability
Collins, 2007
The future state zt+τ is predictable given x if
and only if:
The present state x is observable given y if
and only if:
The estimate of the future state zt+τ is constrained by y :
Emergent Constraint
Observations
Tropospheric Emission Spectrometer (TES)
TES measures high-resolution O3 spectra in 9.6
micron band in order attribute radiance variability to
the atmospheric state that caused that variability.
TES Instantaneous Radiative Kernels (IRK) is the
sensitivity of changes OLR in the 9.6 micron band
to vertical changes in the atmospheric state.
Fig. courtesy M. Mlynzcack (LaRC)
Flux in 9.6 μm flux
O3 IRK
-mW/m2/ln(O3(VMR)
3
W/m2
24
O3
ppb
LWRE
W/m2
Bowman et al, ACP (2013)
ACCMIP OLR9.6μm bias
Bowman et al, ACP (2013)
Good place to look for
emergent constraints
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In the SH subtropics,
discrepancies lead to
over 300 mWm-2 for
individual models and
up to 100 mWm-2 for
the ACCMIP ensemble
relative to TES (20052009). Mean NH bias
is negligible.
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OLR9.6μm bias computed as difference of TES and
ACCMIP ozone project to OLR through the IRK
TES SH ACCMIP RF 2100
ACCMIP radiative
forcing for 2100
RCP 8.5 scenario
taken from
Stevenson et al,
ACP (2013)
R2=0.73
ACCMIP OLR bias
calculated for the
SH from 2005-2009
compared to TES
Strong correlation
between RF 2100
and present day SH
OLR bias
OLR9.6μm from ACCMIP can be computed as
Joint probability RF2100 and SH Flux
linear fit
R2=0.73
p(zt+t | xt = 15 mm)
The linear regression between between RF 2100 and SH OLR implies
a joint Gaussian pdf~N(570,70;15.076,0.042; 0.86)
If present day OLR9.6 μm was known perfectly, then p(RF2100 | OLRi)
would be the most probable RF
How well is OLR9.6 μm known?
Observational constraint on OLR9.6μm
The probability of SH OLR given TES
observations can be calculated using
a data assimiliation perspective:
p(xt | yt ) µ p(yt | xt )p(xt )
The most probable SH OLR:
E[xt | yt ] = x̂t = xt + G(yt - xt )
where the gain and posterior error:
G=
s
(s
2
ACCMIP
2
ACCMIP
+s
2
TES
)
2
ŝ 2 = (1- G)s ACCMIP
s TES = 7(mW/m2 )
s ACCMIP = 42(mW/m2 )
O3 RF in 2100 given TES OLR
Bayesian constraint
ACCMIP RF 2100
given present day
OLR9.6 μm
TES OLR9.6 μm ACCMIP OLR9.6 μm
Emergent constraint on RF2100
Using a similar update formula, the most probable estimate of RF 2100
is
Compared to
How likely is ozone RF greater than the ACCMIP ensemble mean?
How likely is ozone RF greater 500 mW/m2?
)
Balance of precision and accuracy
( /
σ
(
+τ
+τ
(
/
)
)
The uncertainty in ozone RF 2100 given observations is a function
of the error in the observations and the correlation between the present
and future
Summary/Future Directions
•
Emergent constraints within a Bayesian probabilistic (data assimilation)
framework are composed of two steps:
– Correlation between future and present (historic) climate derived from a climate
ensemble
– Observational constraint on the present (historic) climate
•
•
•
Emergent constraint between ACCMIP SH OLR in the 9.6 μm band and radiative
forcing in 2100
TES SH OLR 9.6 μm and IRK constraints lead to a lower a posteriori RF 2100 of 463
± 37 W/m2 compared to a priori 568 ± 70 W/m2 from ACCMIP.
Theoretical framework for emergent constraints is broadly applicable:
– Information content of observing systems should be quantified
•
•
The relationship of emergent correlations versus emergent constraints needs to
be better understood.
Emergent constraints will be enabled by
–
–
comprehensive chemical reanalysis (e.g., Miyazaki, 2013)
new air quality-climate constellation (Bowman, 2013; http://ceos.org/ourwork/virtualconstellations/acc/)
Confidence Intervals
( | )
-
-
-
-
Δα /Δ
Prob{z<-1.2} = 0.07
Prob{z>-0.6} = 0.05
Caveat Emptor
AM-3
MOCAGE
The GFDL AM-3 is consistent with TES SH OLR but has very high RF
2100 while MOCAGE is significantly different from TES SH OLR but
consistent with the lower a posteriori RF 2100 estimate.
Processes controlling AM-3 and MOCAGE RF are significantly different
than the rest of ACCMIP.
IPCC AR5
Radiative forcing from atmospheric composition
Wallington T J et al. PNAS 2010;107:E178-E179
IPCC, AR5
Carbon dioxide, methane, and ozone
are the three most important
greenhouse gases resulting from
anthropogenic activities.
These gases are coupled through
common sources and coupled within
the Earth System.
Arneth et al, 2010, Nat. Geo. Sci.