A Stategy for Predicting Climate Sensitivity Using Satellite Data

1
A Stategy for Predicting Climate Sensitivity
Using Satellite Data Daniel B.
Kirk-Davidoff University of Maryland Department
of Meteorology dankd_at_atmos.umd.edu
2

• Talk Structure
• Background on the Fluctuation Dissipation Theorem
• Experiments using a Toy Model
• Model Description
• Results
• An additional complication
• Preliminary model-data comparison exercise
• Conclusions

3
The Fluctuation Dissipation Theorem
As discussed in Leith (1975), the Fluctuation
Dissipation theorem states that the
infinitessimal impulse-response tensor g(t) is
equal to the lag covariance matrix of the
response lag t, divided by its variance.
Climate change
Typically, the FDT is used to derive macroscopic
properties of a system from a theoretical model
of its statistical properties. Here, the hope
is that by measuring rapid fluctuations over a
relatively short time, we can derive the
long-term climate sensitivity of a model, or of
the real world.
Climate forcing
Time over which U is different from zero
4
Derivation
Starting from a simple stochastic differential
equation
Its not hard to see that the lag autocorrelation
should fall off exponentially
From which it follows that
It turns out, though, that we get better results
by integrating both sides of the second
equation,since this averages over a lot of noise
5
Variations on FDT
1. Cionni et al.s variation
2. Our variation
6
Toy Model

• We next construct a half-dimensional toy model,
  with only surface and atmospheric heat budgets,
  and a gray atmosphere.
• The model can be run very quickly (10 seconds for
  20 years of model time on a laptop computer under
  MATLAB).
• The model sensitivity can be varied by making
  either the atmospheric emissivity or the surface
  albedo functions of temperature, vaguely
  analogous to a water vapor or ice-albedo
  feedback, respectively.
• We force the model with AR1 noise applied to
  either the solar constant or the emissivity
  (anologous to CO2 forcing), and compare
  sensitivities derived using the
  Fluctuation-Dissipation Theorem with the true
  climate sensitity, easily found by running the
  model to equilibrium.

7
Toy Model Variables

• Cs, Ca surface and atmospheric heat capacity
• Ts, Ta surface and atmospheric temperature
• ? albedo
• ?? Stefan-Boltzmann constant
• ? atmospheric longwave emissivity
• ???? base emissivity
• ?0 forced emissivity
• ?S atmospheric short wave absorptivity
• S00 solar constant
• S0 variable insolation
• f???f?? feedback parameters for albedo and
  longwave emissivity
• A AR1 noise, scaled to zero mean, standard
  deviation 1.
• cA AR1 noise parameter
• r Random noise, flat distribution 0-1

8
Toy Model Equations
Surface, atmospheric Energy budgets.
Feedbacks on albedo and emissivity
Forcing of emissivity and insolation
Generation of AR1 noise
9
Equilibrium Climate Sensitivity for a range of
parameter values
10
Model Response to AR1 Solar Forcing
11
Model Response for Various Heat Capacities
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
Toy Model Results

• For sufficiently small heat capacity or
  sufficiently long time series, FDT-based methods
  gives excellent predictions of the relative
  magnitude of model sensitivity.
• The length of the time series necessary for an
  accurate prediction of sensitivity is comparable
  to the models equilibration time scale for a
  given heat capacity.

18
Preliminary model-data comparison

• We look at a forced (1 /year increase in CO2)
  run of NCAR CCSM 2.0
• Use FDT to derive local sensitivity using CO2
  data.
• Compare to sensitivity derived from surface
  temperature and TOA solar forcing.
• Compare this to result for NCEP data.
• Future use IR radiances from multiple channels
  of AIRS data.

19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
Conclusions

• The FDT or related measures based on
  lag-covariances give accurate predictions of
  model sensitivity for a broad range of feedback
  and forcing types.
• The length of the time series required for
  accurate computation of model sensitivity
  increases with the time scale for the approach to
  equilibrium, though this relationship becomes
  complicated when multiple surface heat capacities
  are involved. Thus these measures are likely to
  be useful as a short-cut to evaluating a models
  climate sensitivity.
• However, our results confirm that lag covariances
  are intimately connected to climate sensitivity.
  This suggests that metrics involving lag
  covariance of surface temperature and TOA
  radiative fluxes could be a very powerful metric
  by which to compare models and data, and thus to
  estimate the climate systems true sensitivity to
  radiative forcing.

26
References Bell, T.L., 1980 Climate sensitivity
from fluctuation dissipation Some simple model
tests. J. Atmos. Sci., 37 17001707. Chou,
M.-D., M. J. Suarez, X.-Z. Liang, M. M.-H. Yan,
2001. A thermal infrared radiation
parameterization for atmospheric studies. NASA
Technical Memorandum 104606, vol. 19, 65 pp.
Available at (http// climate.gsfc.nasa.gov/
chou/clirad_lw). Cionni, I., G. Visconti, and F.
Sassi, 2004. Fluctuation dissipation theorem in
a general circulation model. Geophys. Res.
Letts., 31L09206, doi 10.1029/2004GL019739 Emanu
el, K.A., 1991 A scheme for representing
cumulus convection in large-scale models. J.
Atmos Sci., 48 2313-2335. Model code updated by
the author in 1997, available at
ftp//texmex.mit.edu/pub/emanuel/CONRAD. Haskins,
R.D., R.M. Goody, L. Chen, 1997 A statistical
method for testing a general circulation model
with spectrally resolved satellite data. J.
Geophys. Res., 10216,56316,581. Kirk-Davidoff,
D.B., 2005 Diagnosing Climate Sensitivity Using
Observations of Fluctuations in a Model with
Adjustable Feedbacks. Submitted to J. Geophys.
Res. Leith, C.E., 1975 Climate response and
fluctuation dissipation. J. Atmos. Sci., 32
20222026. Acknowledgements This work was
inspired by conversations with John Dykema, Jim
Anderson, Richard Goody and Brian Farrell. It
was made possible by start-up funds provided by
the University of Maryland