Transcript Preliminary Calculation of an Upper Bound to Climate Prediction Skill

Impacts of Systematic Error
Reduction on CAM3.1
Sensitivity to CO2 Forcing
Charles Jackson (1)
Yi Deng (1)
Gabriel Huerta (2)
Mrinal Sen (1)
(1) Institute for Geophysics, The University of Texas at Austin
(2) Department of Statistics, University of New Mexico
In some cases, reducing systematic
errors may not be better.
• There may exist multiple “solutions”
– Non-linearities
– Compensating errors
– Trade-offs
Observed
Nino 3 Index
Histogram
observation
Var = 0.65
Skew = 0.72
Kurt = 4.0
WWSH
cost = 0.024
WWDH
cost = 0.056
SWDH
cost = 0.057
Var = 0.61
Skew=0.92
Kur=3.3
Var=0.65
Skew=0.20
Kurt=3.2
Var =0.74
Skew= 0.92
Kurt = 4.1
WWSH
WWDH
Skewness
Zonal Wind Strength
Variance
Period
Thermocline depth
SWDH
Strength of Noise
Strength of Mean Wind
2D Marginal PPD
Subsurface Sensitivity
Mean thermocline depth (m)
l-1(day)
d
q
H (m)
noise
winds
WWSH
3.7
0.6
0.2
79
1.3
0.8
WWDH
3.3
1.4
0.6
165
3.9
0.6
SWDH
4.0
1.8
0.4
183
1.9
1.2
(IPCC 2001)
Bayesian Stochastic Inversion
Bayes’ Theorem
P(Φ) P( Χ | Φ)
P(Φ | Χ) 
P( Χ)
Ф, parameters; Х, observations;
P(Ф|Х), probability of Ф given X.
Likelihood
P(Х|Ф) = exp(- cost)
small cost ↔ large likelihood
BSI provides a way to sample wide regions of parameter space
and to summarize the results in terms of a relative probability.
Jackson, C., M. K. Sen, and P. L. Stoffa, 2004, J. Climate, 17, 2828-2841
Methods to estimate multidimensional probability distributions
•
•
•
•
Grid Search
Monte Carlo (random sampling)
Metropolis/Gibbs’ Sampler (MCMC)
Bayesian Stochastic Inversion using
multiple Very Fast Simulated Annealing
(Sen and Stoffa, 1996).
Probability density functions for
3 parameters:
VFSA
Grid Search
Metropolis
Metropolis
VFSA
(Jackson et al., JCL 2004)
Definition of cost function
N



1
E (m) 
(dobs - g (m))T C-1(dobs - g (m)) i
2N
i 1
Definition of model-observational data mismatch
(Mu et al., JGR 2004)
E (m) 
N



1
(dobs - g (m))T C-1(dobs - g (m)) i
2N
i 1
(d obs - g ( m)) 
K
 a j  EOF j
j 1
2
1 N  K a j 
E (m) 
2 N i 1  j 1 l2j 

i

Status
• Considering 6 free parameters important
to clouds and (deep) convection
• T42 CAM3.1, forced by observed SST
March 1990 to February 2001.
• ~250 experiments have been completed.
• Of these, ~95 got cost values lower than
the default case.
• Average improvement in cost value is 7%.
Default
Total
Line 1,
gen 48
Line 2,
gen 31
Line 3,
gen 34
Line 4,
gen 43
Line 5,
gen 31
Line 6,
gen 35
~85
81.51
78.84
79.62
79.84
80.69
81.07
CLDLOW
84.46
82.01
81.58
82.82
80.72
84.82
80.76
CLDMED
36.02
35.91
41.18
38.34
40.17
45.45
37.27
CLDHGH
64.56
66.34
69.64
66.90
68.14
72.03
67.26
FSDS
64.04
53.41
55.65
52.57
54.83
59.13
53.21
FSNT
134.30
148.30
142.8
149.7
141.5
132.90
144.4
FLNT
28.90
29.20
29.42
29.01
28.85
31.81
29.33
202.00
121.20
140.3
122.7
142.70
155.70
126.90
TREFHT
43.13
41.60
42.58
42.88
43.12
41.69
42.40
SHFLX
55.62
54.70
55.81
56.02
55.11
54.37
54.64
LHFLX
41.15
39.01
39.49
40.57
39.53
40.27
38.89
RELHUM
236.6
265.20
212.00
225.0
227.70
220.80
258.4
T
171.2
165.70
161.50
170.2
160.00
163.50
163.4
U
37.52
33.40
36.00
35.56
35.63
35.39
35.27
PSL
26.25
24.48
25.06
25.51
25.27
25.29
24.00
PRECT
24.20
21.99
20.21
22.65
20.55
20.78
21.23
BALANCE
climateprediction.net
27,000 experiments completed in past year on 10,000 personal computers
(Stainforth et al., Nature 2005)
(Deng et al., GRL, in press)
Review of results
• BSI was able to identify multiple model
configurations that improved CAM3.1 skill scores
by 7%. (Experiments ongoing, only ¼ way
through to completion.)
• IPCC reports suggest large uncertainties are not
going away…(fundamental?)
– We found surprisingly little spread among models that
explored parameters thought to be sources of
uncertainty.
• Despite agreement at a global scale, parametric
uncertainties lead to significant scatter in
predictions of regional climates.
• Although higher order statistics were not
included in cost function, there were substantial
improvements in predictions of heavy rainfall
rates.