<p>Climate change is a complex, multidisciplinary problem which relates our physical understanding of the consequences of greenhouse gas emissions with economic and socio-political actions to mitigate and adapt to those consequences. An important role that the mathematics of climate change can play involves utilising and developing understanding of nonlinear systems in such a way as to guide the design of ensembles of Global Climate and Earth System Models (ESMs), as well as integrated assessment and economic models. To this end it is informative to view these computer models as high-dimensional nonlinear systems and ask what we can learn about ensemble design from somewhat related, low-dimensional nonlinear systems.</p> <p> </p> <p>This talk will discuss what it means to make a prediction of climate change within a computer model as well as how we can design ensembles to reflect our uncertainty in the real-world, physical climate system. The Lorenz ’84/Stommel ’61 (L84-S61) system will be introduced as a valuable tool for studying issues of ensemble design and will be used to illustrate key sources of uncertainty and sensitivity.</p> <p> </p> <p>First amongst these senstitivities is initial value sensitivity of the sort explored in a variety of single model large ensembles (see session CL4.10/NH11/OS4) - these are known as micro-initial-condition ensembles. However, the results of such ensembles can themselves be dependent on large scale features of the starting conditions - so-called macro-initial-condition uncertainty. Lastly, the sensitivity of ensemble results to model structure and parameter value selection is crucial. How can we identify how close to the target system a model has to be to make useful probabilistic forecasts at different lead times? This question raises the prospect that climate predictions could be vulnerable to the “hawkmoth effect” - the potential for probabilistic forecasts based on initial condition ensembles to be highly sensitive to the finest details of model formulation.</p> <p> </p> <p>Here the different types of initial value and model parameter sensitivities will be illustrated with the L84-S61 system. Based on these, a series of design questions will be raised - questions which suitably-designed ensembles of low-dimensional systems could help us understand and answer, and which could be extremely valuable in improving the design of ensembles of GCMs and ESMs.</p>
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