Ensembles of ensembles of ensembles: On using low-dimensional nonlinear systems to design climate prediction experiments
Authors: Stainforth David 
Published: March 2022

&lt;p&gt;The challenges of climate prediction are varied and complex. On the one hand they include conceptual and mathematical questions relating to the consequences of model error and the information content of observations and models. On the other, they involve practical issues of model and ensemble design, and the statistical processing of data.&lt;/p&gt;&lt;p&gt;A route to understanding the complexity of these challenges is to study them using low-dimensional nonlinear systems that encapsulate the key characteristics of climate and climate change. Doing so facilitates the fast generation of very large ensembles with a variety of designs and target goals. These idealised ensembles can provide a solid foundation for improving the design of ESM/GCM ensembles, making them better suited to evaluating the risks associated with climate change and to providing end-user support through climate services.&lt;/p&gt;&lt;p&gt;The ODESSS project - Optimizing the Design of Ensembles to Support Science and Society - is using low-dimensional nonlinear systems to provide solid foundations for the design of climate change ensembles with climate models. In this presentation I will introduce the project and the concepts behind it.&lt;/p&gt;&lt;p&gt;First I will discuss the essential characteristics required of a low dimensional nonlinear system to be able to capture the process of climate prediction. Results will then be presented from the coupled Lorentz &amp;#8217;84 - Stommel &amp;#8217;61 system; a low-dimensional nonlinear system which has these characteristics. These results will be used to illustrate the dangers of confounding natural variability with the consequences of initial condition uncertainty[1], and to demonstrate why risk assessments require much larger initial condition ensembles than are currently available with today&amp;#8217;s ESMs/GCMs.&lt;/p&gt;&lt;p&gt;The difference between micro and macro initial condition ensembles [2,3] will then be introduced, along with an explanation of how this leads to a requirement for ensembles of ensembles: the former exploring macro-initial-condition-uncertainty, the latter micro-initial-conditional-uncertainty. The importance of this distinction will be illustrated with both new results from the Lorentz &amp;#8216;84 - Stommel &amp;#8216;61 system, and also a GCM[3]. I will highlight the challenges in designing these ensembles of ensembles to be most informative. These challenges relate closely to the problems of initialization and the optimal use of observations.&lt;/p&gt;&lt;p&gt;Finally the subject of model error, multi-model and perturbed-physics ensembles will be discussed. The impact of model error on climate predictions can only be studied effectively if climate change can be accurately quantified within each model. To begin to explore the consequences of model error for climate predictions therefore requires ensembles of ensembles of ensembles: perturbed-physics or multi-model ensembles which&amp;#160; themselves consist of both macro and micro initial condition ensembles. Some approaches will be presented for how low-dimensional systems can be used to optimise the design of such multi-layered ensembles with ESMs/GCMs where computational constraints are more restrictive.&lt;/p&gt;&lt;p&gt;[1] Daron and Stainforth, &lt;em&gt;On predicting climate under climate change&lt;/em&gt;. ERL, 2013.&lt;/p&gt;&lt;p&gt;[2] Stainforth et al., &lt;em&gt;Confidence, uncertainty and decision-support relevance in climate predictions&lt;/em&gt;. Phil. Trans Roy. Soc., 2007.&lt;/p&gt;&lt;p&gt;[3] Hawkins et al., &lt;em&gt;Irreducible uncertainty in near-term climate projections&lt;/em&gt;. Climatic Change, 2015.&lt;/p&gt;