# RCPM - About the Method

## Overview

RCPM (**R**egional **C**limate-Change **P**rojection from
**M**ulti-Model Ensembles) is a statistical analysis of the
projections made by different climate models.

We use a Bayesian statistical model to synthesize the information in an ensemble of global climate models (GCMs) into a probability density function (PDF) of change in temperature or precipitation for a given geographic region.

A PDF describes the likelihood that an unknown variable will take on a value found within a particular range. Bayesian analysis uses known data to infer probabilistic values for unknown data that are consistent with the known values. This allows us to infer the reliability of the models' forecasts for the future (which is unknown) based on their ability to reproduce observed data and their agreement with one another (both of which are known).

In generating the PDF, the analysis assigns an implicit weight to each model's contribution based on two factors: bias and convergence. A model's bias is assessed by comparing its reproduction of the current climate to observed historical data, averaged over a region and season of interest. Convergence among models is rewarded by giving relatively more weight to projections that agree with the other members of the ensemble than to outliers. Because agreement between models may be due to model dependence, the analysis downweights the convergence criterion relative to the bias criterion.

We perform this analysis at a regional scale, area-averaging data from several gridpoints into regional means of temperature and precipitation. For any given season and emissions scenario, we then use the Bayesian model to determine a PDF of temperature and precipitation change. A season is any set of one or more consecutive months up to a year; the available emissions scenarios are SRES scenarios A2 (high), A1B (midrange), and B1 (low emisssions); and change is the difference between two 20-year averages, for example 1980-1999 (the typical "current climate" period) versus 2080-2099.

## Caveats and Cautions

- The uncertainty range as represented by our PDFs does not encompass all the uncertainties that characterize climate change projections, especially at regional scales. In particular:
- The PDFs are conditional on the specified emissions scenario. We do not assign probabilities to the different scenarios.
- Generally speaking, the projections are conditional on the GCMs used. We acquired GCMs from the PCMDI archive organized by IPCC Fourth Assessment Report (AR4) participants. These GCMs are state-of-the-art coupled climate models, but each of them carries considerable uncertainty in its parameterizations and in its represenation of processes and dynamics, especially at regional scales. These uncertainties have not been explicitly incorporated into the analysis.
- For regions of complex topography and small extent, the preceding caveat is even more significant than it is for large areas over smooth terrain. Consequently, an area encompassing 4 gridpoints (a gridpoint is approximately 2.8 degrees on each side) is the minimum extent that we are comfortable addressing using this framework.
- PDFs are normalized so the area under the curve integrates to 1.
It is only meaningful to speak of probabilities for a range of
possible values (e.g., 60% probability of warming
*between 2 and 4 degrees*), not for a single value. - Changes in temperature and precipitation are derived separately; the quantiles of one distribution should not be associated with the corresponding quantiles of the other.
- Change in precipitation is presented in both absolute and relative amounts. Percent change values for areas with low precipitation can be very large even though the absolute change is small.
- Each model's grid has been interpolated to the median resolution of the available models, the T42 gaussian grid. This grid covers the globe with 64 gridpoints in latitude and 128 gridpoints in longitude.

## Suggestions for Use

It is important not to think of these projections as a crystal ball that gives you a vision of the future. The best way to use these results is to get a sense of what the range of likely outcomes is given a particular assumption about emissions, and to incorporate that uncertainty (as well as uncertainty about emissions) into your thinking about future climate. Use them as probable guidelines, not certain forecasts: think in terms of bounding the set of likely scenarios, rather than picking a single characteristic outcome.

## Explanation of the Bayesian Statistical Model

The Bayesian analysis approach is motivated by work done by Giorgi and Mearns; see References for a link to the original paper.

In the Bayesian framework, we treat the quantities whose uncertainties we want to characterize — the temperature under current and future conditions and the reliability of the GCMs in reproducing these climates — as random parameters and hypothesize a prior distribution for them.

Then we formulate the likelihood of occurrence of the data (the observed and modeled temperatures) conditional on the value of the parameters. We combine these two components using Bayes' theorem to get a joint posterior distribution for all uncertain parameters, including those whose difference represents change in temperature. We estimate this posterior distribution using a Markov chain Monte Carlo algorithm. Precipitation is analyzed analogously.

The statistical assumptions are formulated such that the two criteria of GCM reliability, bias and convergence, influence the final result through the weighting of the members of the multi-model ensemble in the posterior distribution of climate change. The bias criterion is a measure of how well a model reproduces present-day climate, while the convergence criterion is a measure of how well a model's future projection agrees with those of the other models. The regional nature of the analysis means that these two criteria are evaluated for each model only with respect to the region of interest, not at a global scale.

This method is only one of many for creating a probabilistic climate projection from an ensemble of different models. Refer to the paper by Tebaldi & Knutti for an overview of other methods.

## References

For more details on a subject, please refer to the following articles:

*Statistical formulation and derivation of the PDFs through Markov
Chain Monte Carlo simulation:*

C. Tebaldi, R. L. Smith, D. Nychka and L.O. Mearns (2005) Quantifying
uncertainty in Projections of Regional Climate Change: a Bayesian
Approach to the Analysis of Multimodel Ensembles. *Journal of Climate,*
vol. 18, no. 10, pp. 1524-1540. link

C. Tebaldi, L.O. Mearns, D. Nychka and R. L. Smith (2004) Regional
probabilities of precipitation change: A Bayesian analysis of
multimodel simulations. *Geophysical Research Letters,* v. 31. link

*Work by Giorgi and Mearns motivating the use of Bayesian
analysis:*

Giorgi F., and L. O. Mearns (2002) Calculation of Average,
Uncertainty Range, and Reliability of Regional Climate Changes from
AOGCM Simulations via the "Reliability Ensemble Averaging" (REA)
method. *Journal of Climate*, vol. 15, no. 10, pp. 1141-1158. link

*Overview of different methods of probabilistic climate
projection using multi-model ensembles:*

Tebaldi, C. and R. Knutti (2006) The use of the multi-model
ensemble in probabilistic climate projections. *Philosophical
Transactions of the Royal Society A*, vol. 365, pp. 2053-2075
(2007) pdf