# Presentation: 856787

## Performance-based multimodel probabilistic climate change scenarios

- Arthur M. Greene, Lisa Goddard, Upmanu Lall
- International Research Institute for Climate Prediction
- The Earth Institute at Columbia University
- Palisades, NY
- amg@iri.columbia.edu

## Goal: Production of regional climate outlooks for the coming century
Initial focus: Evolution of mean regional temperatures; eventually continuing with variability, precipitation...
Methodology: Multimodel ensemble, combined in the framework of a linear Bayesian probability model
Coefficients derived by fitting to simulations of 
	20th-century climate (20C3M runs from IPCC AR4)
Bayesian estimation employed, in keeping with probabilistic framework
Model formulations with varying degrees of complexity explored

- Initial focus: Evolution of mean regional temperatures; eventually continuing with variability, precipitation...
- Methodology: Multimodel ensemble, combined in the framework of a linear Bayesian probability model
- Coefficients derived by fitting to simulations of
- 	20th-century climate (20C3M runs from IPCC AR4)
- Bayesian estimation employed, in keeping with probabilistic framework
- Model formulations with varying degrees of complexity explored

## Regional definitions as in the IPCC SAR...

## AOGCMs may exhibit significant regional temperature biases

- Central American sector (CAM), raw temperature series

- Anomalies (relative to each model’s 1961-1990 climatology)

- Obs

## Incoherence not limited to interannual variations

## Mean regional temperatures are simulated with more fidelity than are regional temperature trends. 

- Regional annual mean T, 1961-1990

- Regional annual-mean T trends, 1965-1998

## Probability model structures compared

- A			     (variance of Y is uniform...)
- B:			     (or regionally dependent...)
- C:			        (cov(**) modeled explicitly)
- The last of these represents a multilevel, or hierarchical structure:
- 1: Regional series of obs and simulations
- 2: Global structure for parent distribution of **
- Priors are “diffuse” (i.e. non-informative) with the qualified exception of ****for which a scale matrix must be specified to at least an order of magnitude.

## Probability model C as a graph (DAG)

- years i

- regions k

- models j

## Regional input covariance exhibits varying degrees of structure...

## Some model comparison statistics (mean annual temperature)

| Model | Dbar | Dhat | DIC | pD |
| --- | --- | --- | --- | --- |
| A | 2532 | 2217 | 2847 | 315.3 |
| B | 1768 | 1429 | 2108 | 339.4 |
| C | 1735 | 1505 | 1964 | 229.8 |

- Dbar: Mean of the posterior deviance: 		mean (-2 log(p(y|)))
- Dhat: Posterior deviance computed from mean :	-2 log(p|(y|bar))
- DIC: “Deviance Information Criterion,” an estimate of predictive skill.
- pD: Effective number of parameters in the model.

- Conclusion: Model B a lot better than A; C a little better than B

## Some fitted series...

- Model A

- Model B

## Fitted series, cont'd

- Model B

- Model C

## Model structure and estimation of jk

## Prior distribution of cov() is “imprinted” by the data

- Prior correlation for 
- A blank slate

- Posterior correlation:
- (Weak) structure is present

## Cross-validation

| Season | F | P (1=2=198) |
| --- | --- | --- |
| Ann | 4.38 | 1.16E-23 |
| DJF | 2.58 | 3.05E-11 |
| JJA | 3.32 | 1.22E-16 |

- Computed with respect to decadal means
- “Leave-10-out”, with model fitted to remaining data. Nine values / region

- Comparison over all regions

- Region by region (annual mean)

## DJF, JJA...

## Coefficients are applied to the SRES scenario simulations to generate the final temperature projections

## Stationarity assumptions cannot be ignored...

## Summary

- Regional temperature projections are generated for the 21st century
- Based on IPCC 20C3M experiments, SRES scenario simulations
- AOGCM outputs combined in the framework of a Bayesian hierarchical linear model of limited complexity
- Relaxation of constraint that	         	 allows resultant to “escape the envelope” of the underlying simulations
- Projections appear to be an improvement over the unweighted mean of the contributing AOGCMs. This improvement is greatest for the annual mean, decreasing but still present for DJF and JJA
- There is an implicit assumption of stationarity, and with this comes the unavoidable responsibility of choosing good (or at least defensible) assumptions in model building. So what else is new?