Characterising and comparing different palaeoclimates with dynamical systems theory

Numerical climate models have long been used in the study of the Earth’s palaeoclimate – the climate in ancient times before modern instrumental records. Examples range from early investigations based on simple thermodynamic or general circulation models to the modern state-of-the-art models now being used in the Paleoclimate Modelling Intercomparison Project. Compared to typically low-resolution and geographically sparse data held in from palaeo-archives, numerical climate simulations produce a vast amount of data with high spatial and temporal resolution. The resolution and complexity of numerical models has also greatly increased in recent years, along with the amount of data they produce. All of this poses new challenges to the palaeoclimate community, raising questions of how to efficiently process and interpret model outputs.
The significant uncertainties often found in palaeo- simulations present a distinct but related challenge. These reflect the uncertainties present in existing palaeo-archives, as well as in our knowledge of the appropriate boundary conditions and forcings affecting past climates. Because of these uncertainties, different simulations of the climate for the same period and region may yield very different results. This problem emerges both in reconstructions of climates from millions of years ago, such as the mid-Pliocene warm period over 3 Myr BP as well as in climates in more recent times such as the mid-Holocene around 6000 yr BP. Understanding these discrepancies, and appreciating their significance, requires analysis tools attuned to drawing out the key differences between distinct simulated palaeoclimates.
In a recent Technical Note, LML Fellow Davide Faranda and Gabriele Messori consider these issues, and propose a framework for efficiently processing and interpreting large amounts of model output to compare different simulated palaeoclimates. Their approach is grounded in dynamical systems theory, and allows researchers to characterise the dynamics of a given dynamical system – the atmosphere, for example – using three one-dimensional metrics. A first metric estimates the persistence of instantaneous states of the system. A second metric, which they call the “local dimension,” provides information on how the system evolves toward or away from instantaneous states. Finally, the third metric – the co-recurrence ratio – is a measure applicable to two (or more) variables, which quantifies their instantaneous coupling. Climate models commonly produce dynamical information embedded in 3-dimensional (latitude, longitude and time) or 4-dimensional (latitude, longitude, pressure level and time) data. For analysis purposes, the authors argue, such data can be projected onto these three metrics, each taking a single value for every time-step in the data. These may then be interpreted and compared with comparative ease.
As the authors note, the dynamical systems metrics they propose can be particularly helpful when processing large datasets. As a practical example, they analyse three numerical simulations of the mid-Holocene climate over North Africa. These include a control simulation with pre-industrial vegetation and atmospheric dust loading, a Green Sahara simulation with shrubland imposed over a broad swath of what is today the Sahara desert, and a different Green Sahara simulation which additionally features heavily reduced atmospheric dust loading. The examples illustrate how the different hydroclimates in these simulations correspond to different dynamical properties of the modelled climate systems, which are captured by the three dynamical systems metrics. The metrics further capture the differences between the simulations, and may be exploited to formulate hypotheses on their physical drivers, such as modulations in atmospheric wave activity.
The article is available at

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