Climate predictions: the influence of nonlinearity and randomness

Abstract

The current threat of global warming and the public demand for confident projections of climate change pose the ultimate challenge to science: predicting the future behaviour of a system of such overwhelming complexity as the Earth's climate. This Theme Issue addresses two practical problems that make even prediction of the statistical properties of the climate, when treated as the attractor of a chaotic system (the weather), so challenging. The first is that even for the most detailed models, these statistical properties of the attractor show systematic biases. The second is that the attractor may undergo sudden large-scale changes on a time scale that is fast compared with the gradual change of the forcing (the so-called climate tipping).Keywords: stochastic closure; climate tipping; statistical modelling; time-series analysis; thermodynamicsThe current threat of global warming and the public demand for confident projections of climate change pose the ultimate challenge to science: predicting the future behaviour of a system of such overwhelming complexity as the Earth's climate. In principle, the Earth's climate could be viewed as a deterministic dynamical system. The laws of motion (such as the fluid dynamics of ocean and atmosphere), and the time-dependent forcing (mostly insolation, but also interactions, for example, with the biosphere or geothermal sources) are known such that one ends up with a large system of differential equations determining the future state entirely, using the current state as initial condition. Unfortunately, as Lorenz [1] demonstrated with a simple model for convection, this statement, even though true in principle, is not applicable in practice. In chaotic systems, trajectories from nearby initial conditions diverge from each other at an exponential rate such that the future state becomes unpredictable beyond a time horizon determined *Author for correspondence (jan.sieber@port.ac.uk). Thompson and J. Sieber by the divergence rate. In the face of this problem, the intuitive justification for attempting long-term climate prediction is that, while the weather is clearly chaotic, the climate is representing the attractor of this chaotic system. If the chaotic attractor is well-behaved and the model simulations are unbiased then ensemble runs of these simulations can reveal the statistical properties of the attractor (for example, mean, variability and frequency of extreme events). Moreover, one may hope that gradual changes in the forcing or system parameters lead to a gradual change of the attractor and its statistical properties. This approach would treat the short-term chaos as noise, thus, making predictions about the statistical properties of realizations of this noise on long time scales. Gradual changes of the forcing can be either man-made (for example, in an emission scenario) or external (for example, astronomical, if one learns from the behaviour of the palaeoclimate).This Theme Issue addresses two practical problems that make even this type of statistical prediction ...

On the scaling effect in global surface air temperature anomalies

“…The observed poleward stronger persistence in LSAT could be in general a result of either stronger positive feedbacks or larger inertia. In addition, the scaling property detected in the in-field observations of the LSAT anomalies could serve as a test for the state-of-the-art and the scaling performance of the advanced global climate models for confident projections of climate change (e.g., Theme Issue, Thompson and Sieber, 2012).…”

The Impact of Climate Change on Hydro-Meteorological Droughts in the Chao Phraya River Basin, Thailand

“…It is important to note that, while the empirical quantile mapping method was proven to perform satisfactorily for this study, the results could be sensitive to the choice of calibration time period [78]. The choice of the best RCM may then be altered when the future state of climate becomes unpredictable due to several factors involving a chaotic system, such as uncertainty, randomness, and the divergence from initial conditions as it moves beyond a time horizon [79,80]. Thus, the robustness of the bias correction method applied here cannot be guaranteed and it is less decisive on the choice of the RCM.…”

“…The agreement in this tendency was for all RCMs, as seen in Figure 11, Figure A3, and Figure A4. The cause of these fluctuations is unclear, but it is probably due to the randomness that is typically associated with the inherent unpredictability of future climate phenomena [79,81].…”

Increasing Long-Term Memory as an Early Warning Signal for a Critical Transition

“…In recent years, with the development of science and technology and the deepening of human understanding about the mechanisms of climate change, the simulation performance and prediction skills of various numerical models have been continuously improved. However, due to the nonlinear and complex characteristics of climate systems, it is still difficult to accurately predict abrupt climate change through the numerical models at present (Thompson and Sieber 2012).…”