1. 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
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

2. 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?

3. 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?

4. Emergent constraints
An emergent constraint are based upon two factors:
A correlation between future and historic climate, which is frequently determined through a climate model ensemble.
Observations of historic climate.
What is the joint distribution of the future and the present given observations of the present?
where
is the future state at t+τ
is the current state at t
are the observations at t

5. Predictability and Observability
The future state zt+τ is predictable given x if and only if:
Collins, 2007
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

6. 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 O3
LWRE
-mW/m2/ln(O3(VMR)
ppb
W/m2 3
W/m2 24
Bowman et al, ACP (2013)

7. ACCMIP OLR9.6μm bias
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 ( ). Mean NH bias is negligible.
Bowman et al, ACP (2013)
OLR9.6μm bias computed as difference of TES and ACCMIP ozone project to OLR through the IRK
Good place to look for emergent constraints

8. 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 compared to TES
Strong correlation between RF 2100
and present day SH OLR bias
OLR9.6μm from ACCMIP can be computed as

9. Joint probability RF2100 and SH Flux
linear fit
R2=0.73
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?

10. Observational constraint on OLR9.6μm
The probability of SH OLR given TES
observations can be calculated using a data assimiliation perspective:
The most probable SH OLR:
where the gain and posterior error:

11. O3 RF in 2100 given TES OLR ACCMIP RF 2100 given present day OLR9.6 μm
Bayesian constraint
ACCMIP RF 2100 given present day OLR9.6 μm
TES OLR9.6 μm
ACCMIP OLR9.6 μm

12. 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 than the ACCMIP ensemble mean?
How likely is ozone RF greater 500 mW/m2?

13. Balance of precision and accuracy
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

14. 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;

15. Confidence Intervals
Prob{z<-1.2} = Prob{z>-0.6} = 0.05

16. 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.

17. Radiative forcing from atmospheric composition
IPCC AR5
IPCC, AR5
Wallington T J et al. PNAS 2010;107:E178-E179
well mixed, longer lived gases (CO2, CH4, N2O) considered “high” in scientific understanding
large uncertainties in pre-industrial ozone distributions
also significant uncertainties in spatial/temporal variability of ozone, and indirect forcing from emission predictions for ozone precursors with corresponding non-linear chemistry.
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.