Sensitivity analysis of the climate of a chaotic system

By D. Lea, Myles Allen, Thomas W. N. Haine. 2000

237 citations recorded by the source corpus.

This paper addresses some fundamental methodological issues concerning the sensitivity analysisof chaotic geophysical systems. We show, using the Lorenz system as an example, that anaïve approach to variational (“adjoint”) sensitivity analysis is of limited utility. Applied totrajectories which are long relative to the predictability time scales of the system, cumulativeerror growth means that adjoint results diverge exponentially from the “macroscopic climatesensitivity” (that is, the sensitivity of time-averaged properties of the system to finite-amplitudeperturbations). This problem occurs even for time-averaged quantities and given infinite computingresources. Alternatively, applied to very short trajectories, the adjoint provides an incorrectestimate of the sensitivity, even if averaged over large numbers of initial conditions, becausea finite time scale is required for the model climate to respond fully to certain perturbations.In the Lorenz (1963) system, an intermediate time scale is found on which an ensemble ofadjoint gradients can give a reasonably accurate (O(10%)) estimate of the macroscopic climatesensitivity. While this ensemble-adjoint approach is unlikely to be reliable for more complexsystems, it may provide useful guidance in identifying important parameter-combinations to beexplored further through direct finite-amplitude perturbations.

Subfields: Condensed Matter Physics, Global and Planetary Change, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/441dea4639ecbd17f805ac9389e261abd185f7fa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

Sam Schoenholz

In Global and Planetary Change

In Statistical and Nonlinear Physics

Citations in the corpus

Effective adjoint approaches for computational fluid dynamics (2019, background): “Moreover, the chaotic nature of turbulent flow poses the fundamental challenge that a small perturbation in the initial conditions may be amplified exponentially at some finite steps and eventually degrade the adjoint derivatives [132].”
Data Assimilation for Numerical Weather Prediction: A Review (2009, background): “Usual methodologies of variational adjoint parameter estimation in NWP do not carry over to climate simulation Lea et al.[192,193] and a combination of approaches is necessary to account for nonlinear feedbacks and uncertainties when tuning multiple multiscale parameters against observations.”
Gradients are Not All You Need (2021, background): “This concept was ﬁrst proposed in [Lea et al., 2000] and improved upon by the space-split sensitivity algorithm (S3) [Chandramoorthy and Wang, 2021] to have better convergence rates.”