## The Annals of Applied Statistics

### Temperatures in transient climates: Improved methods for simulations with evolving temporal covariances

#### Abstract

Future climate change impacts depend on temperatures not only through changes in their means but also through changes in their variability. General circulation models (GCMs) predict changes in both means and variability; however, GCM output should not be used directly as simulations for impacts assessments because GCMs do not fully reproduce present-day temperature distributions. This paper addresses an ensuing need for simulations of future temperatures that combine both the observational record and GCM projections of changes in means and temporal covariances. Our perspective is that such simulations should be based on transforming observations to account for GCM projected changes, in contrast to methods that transform GCM output to account for discrepancies with observations. Our methodology is designed for simulating transient (nonstationary) climates, which are evolving in response to changes in CO$_{2}$ concentrations (as is the Earth at present). This work builds on previously described methods for simulating equilibrium (stationary) climates. Since the proposed simulation relies on GCM projected changes in covariance, we describe a statistical model for the evolution of temporal covariances in a GCM under future forcing scenarios, and apply this model to an ensemble of runs from one GCM, CCSM3. We find that, at least in CCSM3, changes in the local covariance structure can be explained as a function of the regional mean change in temperature and the rate of change of warming. This feature means that the statistical model can be used to emulate the evolving covariance structure of GCM temperatures under scenarios for which the GCM has not been run. When combined with an emulator for mean temperature, our methodology can simulate evolving temperatures under such scenarios, in a way that accounts for projections of changes while still retaining fidelity with the observational record. The emulator for variability changes is also of interest on its own as a summary of GCM projections of variability changes.

#### Article information

Source
Ann. Appl. Stat., Volume 10, Number 1 (2016), 477-505.

Dates
Received: July 2015
Revised: January 2016
First available in Project Euclid: 25 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1458909924

Digital Object Identifier
doi:10.1214/16-AOAS903

Mathematical Reviews number (MathSciNet)
MR3480504

Zentralblatt MATH identifier
1358.62111

#### Citation

Poppick, Andrew; McInerney, David J.; Moyer, Elisabeth J.; Stein, Michael L. Temperatures in transient climates: Improved methods for simulations with evolving temporal covariances. Ann. Appl. Stat. 10 (2016), no. 1, 477--505. doi:10.1214/16-AOAS903. https://projecteuclid.org/euclid.aoas/1458909924

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#### Supplemental materials

• Supplement A: Details on inference and computation, and additional figures. Additional details on estimating the mean changes in temperatures used in model (6) and the simulation (4); details on estimating the components $\delta_{l0}$ and $\delta_{l1}$ in model (6) and their associated standard errors; details on computing the proposed simulation; additional figures exploring the GCM projected variability changes and comparing the GCM output with the observational record; and a description of an animation of the proposed simulation.
• Supplement B: Animation of global simulation. An animation of the proposed simulation.