On quantifying the climate of the nonautonomous Lorenz-63 model

The Lorenz-63 model has been frequently used to inform our understanding of the Earth's climate and provide insight for numerical weather and climate prediction. Most studies have focused on the autonomous (time invariant) model behaviour in which the model's parameters are constants. Here, we investigate the properties of the model under time-varying parameters, providing a closer parallel to the challenges of climate prediction, in which climate forcing varies with time. Initial condition (IC) ensembles are used to construct frequency distributions of model variables, and we interpret these distributions as the time-dependent climate of the model. Results are presented that demonstrate the impact of ICs on the transient behaviour of the model climate. The location in state space from which an IC ensemble is initiated is shown to significantly impact the time it takes for ensembles to converge. The implication for climate prediction is that the climate may—in parallel with weather forecasting—have states from which its future behaviour is more, or less, predictable in distribution. Evidence of resonant behaviour and path dependence is found in model distributions under time varying parameters, demonstrating that prediction in nonautonomous nonlinear systems can be sensitive to the details of time-dependent forcing/parameter variations. Single model realisations are shown to be unable to reliably represent the model's climate; a result which has implications for how real-world climatic timeseries from observation are interpreted. The results have significant implications for the design and interpretation of Global Climate Model experiments.