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 IndexHistogram observation WWSH SWDH WWDH Var = 0.65 Skew = 0.72 Kurt = 4.0 Var = 0.61 Skew=0.92 Kur=3.3 Var =0.74 Skew= 0.92 Kurt = 4.1 Var=0.65 Skew=0.20 Kurt=3.2 cost = cost = cost = 0.057

Skewness Variance Period WWSH WWDHSWDH Thermocline depth Zonal Wind Strength

Mean thermocline depth (m) Strength of Mean Wind 2D Marginal PPD  (day)  H (m) noisewinds WWSH WWDH SWDH Subsurface Sensitivity Strength of Noise

(IPCC 2001)

Bayesian Stochastic Inversion Bayes’ Theorem Ф, parameters; Х, observations; P(Ф|Х), probability of Ф given X. Likelihood Jackson, C., M. K. Sen, and P. L. Stoffa, 2004, J. Climate, 17, BSI provides a way to sample wide regions of parameter space and to summarize the results in terms of a relative probability. P(Х|Ф) = exp(- cost) small cost ↔ large likelihood

Methods to estimate multi- dimensional 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 Metropolis VFSA Metropolis Grid Search (Jackson et al., JCL 2004)

Definition of cost function

Definition of model-observational data mismatch (Mu et al., JGR 2004)

Status Considering 6 free parameters important to clouds and (deep) convection T42 CAM3.1, forced by observed SST March 1990 to February ~250 experiments have been completed. Of these, ~95 got cost values lower than the default case. Average improvement in cost value is 7%.

DefaultLine 1, gen 48 Line 2, gen 31 Line 3, gen 34 Line 4, gen 43 Line 5, gen 31 Line 6, gen 35 Total~ CLDLOW CLDMED CLDHGH FSDS FSNT FLNT BALANCE TREFHT SHFLX LHFLX RELHUM T U PSL PRECT

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.