# Robust Climate Projections and Stochastic Stability of Dynamical Systems (2007-2010)

Principal Investigators: Profs. Michael Ghil (Lead PI), James C. McWilliams and J. David Neelin (Co-PIs), all at IGPP, UCLA, CA 90095, and Ilya Zaliapin (Co-PI), Mathematics & Statistics Dept., Univ. of Nevada, Reno, NV 89557

Collaborators: Mickaël Chekroun, Dmitri Kondrashov, Eric Simonnet

Objectives: The main objective of this proposal is to develop methods for reducing the range of projections in future climate change and increasing the confidence in these projections. This objective is to be achieved by (i) increasing the fundamental understanding of the reason for discrepancies between the simulations of past and current climate, as performed by distinct models or by different versions of the same model; and (ii) based on this understanding, analyze the range of future climate projections and devise tools for systematically reducing it.

Description: The present proposal relies heavily on the substantial advances produced by the effort funded under the P.I.’s former SciDAC project (DE-FG02-01ER63251, “Predictive Understanding of the Oceans’ Wind-Driven Circulation on Interdecadal Time Scales”). The latter project demonstrated that dynamical systems concepts and methods could guide the study of interdecadal climate variability, across a full hierarchy of oceanic and coupled ocean-atmosphere models.

The proposed project strikes out in a new and bold direction, though, and tackles the key issue of the range of uncertainties still left after four assessment reports of the United Nations’ Intergovernmental Panel on Climate Change (IPCC), starting in 1991 and ending in 2007. Rather than limiting itself to a specific area of uncertainty, such as intrinsic variability of the oceans or cloud- radiation interactions, it attacks the fundamental issue of robustness of dynamical systems in general, while focusing on climate models in particular.

The methods are those of the theory of dynamical systems, deterministic and stochastic, including those of parameter estimation and model optimization. We draw on results about the lack of structural stability of deterministic dynamical systems in general, and apply preliminary results on the stabilizing effects of random perturbations on the robustness of certain statistical properties of the perturbed systems. These methods will be applied systematically across a hierarchy of models.

Simple models, to which the theoretical results can be applied directly, will be used to test a number of ideas that extend the known theoretical results and point to practical methods for more realistic models. In selecting these simple models, we will concentrate on specific features of climate variability on inter-annual and inter-decadal time scales. Intermediate models with considerable climatic realism will be optimized in a systematic way and used to check the sensitivity of the range of predictions to changes in parameters. These intermediate models will be chosen among those that are widely tested and accepted as computationally efficient but recognizably related to general circulation models (GCMs). Finally, existing single-model and multi-model ensembles of climate simulations and projections will be examined to verify to which extent the results from the intermediate models can be used to systematically optimize and test the sensitivity of IPCC-class coupled GCMs.

Potential impacts include the development of a strategy for replacing the ad hoc “tuning” of GCMs, used so far by the climate modeling community, by a systematic approach for their optimization, including an a priori estimate of their sensitivity. Such a strategy could modify the approach to future IPCC assessment reports, greatly enhance the robustness of their climate projections, and improve the confidence of decision makers and the public in these projections.

Similar issues of robustness arise in many other areas of the physical and life sciences. The results obtained for climate models could help resolve similar difficulties in population dynamics, epidemiology, macroeconomics and other areas. Given the close interaction between mathematics, physical sciences, statistics and numerical methods that the project involves, a major benefit will accrue to its junior participants in terms of their effectiveness across disciplinary boundaries.

Last but not least, the methods for systematic optimization and sensitivity study involved in the project are intrinsically parallelizable and scalable. These methods can thus directly take advantage of future architectures and increases in computer power contemplated by SciDAC.

### Invited and contributed talks and posters

#### 2007

• TCD participation in the DOE-CCPP meeting , Sept. 2007

#### 2008

• Invited talk at Joint Mathematics Meetings 2008, January 6–9, San Diego.
• Invited talk at the Climate Seminar, Harvard, 6 March 2008.
• Invited talk at the American Physical Society Mtg., March 2008, New Orleans.

#### 2009

• Lecture and poster at winter school on “Reducing the uncertainty in the prediction of global warming”, January 2009, Jerusalem, Israel.
• TCD participation in the DOE-CCPP meeting , April 2009
• Poster at EGU General Assembly, April 2009

#### 2010

• TCD participation in the DOE Climate Change Modeling Programs - Integrated Science Team Meeting. April 2010

#### 2011

• TCD Participation in the European Geosciences Union, General Assembly 2011

### Publications

• I. Zaliapin, and M. Ghil (2010) “Another look at climate sensitivity,” Nonlin. Processes Geophys., 17, 113-122, 2010.
• I. Zaliapin and M. Ghil (2010) “A delay differential model of ENSO variability, Part 2: Phase locking, multiple solutions, and dynamics of extrema,” Nonlin. Proc. Geophys., 17, 123–135.
• Y. Feliks, M. Ghil, and A. W. Robertson, (Revised, PDF Text, Figs., 2010) “Oscillatory climate modes in the Eastern Mediterranean and their synchronization with the North Atlantic Oscillation,” J. Clim., accepted.
• M. Chekroun, E. Simonnet, M. Ghil (2011) “Stochastic Climate Dynamics: Random Attractors and Time-dependent Invariant Measures ,” Physica D, 240 (21), 1685–1700, doi:10.1016/j.physd.2011.06.005.
• L. Roques and M. D. Chekroun (2009)(PDF file) “Does reaction-diffusion support the duality of fragmentation effect?” Ecological Complexity, in press.
• Zaliapin, I., E. Foufoula-Georgiou, and M. Ghil (2009) (PDF file) “Transport on river networks: A dynamical approach,” J. Geophys. Res.-Earth Surface, Special Issue on “Stochastic Transport and Emergent Scaling on the Earth’s Surface,” doi:10.1029/2009JF001281, in press.
• Ghil, M., M. D. Chekroun, and E. Simonnet (2008) (PDF file) “Climate dynamics and fluid mechanics: Natural variability and related uncertainties,” Physica D, invited survey paper for Special Issue on The Euler Equations: 250 Years On”, Physica D, 237, 2111-2126, doi:10.1016/j.physd.2008.03.036 , available online.
• Hillerbrand, R., and M. Ghil (2008)(PDF file) “Anthropogenic climate change: Scientific uncertainties and moral dilemmas,” Physica D, invited paper for Special Issue on The Euler Equations: 250 Years On”, Physica D, 237, 2132-2138, doi:10.1016/j.physd.2008.02.015 , available online.
• M. Ghil, I. Zaliapin, and S. Thompson (2007) (PDF File). “A delay differential model of ENSO variability: Parametric instability and the distribution of extremes,” Nonlin. Proc. Geophys., 15, 417 – 433.
• J. C. McWilliams (2007) (PDF File, online access) “Irreducible imprecision in atmospheric and oceanic simulations ,” PNAS, 104(21), 8709 – 8713.