A New Algorithm for Low-Frequency Climate Response

Abstract

Abstract The low-frequency response to changes in external forcing for the climate system is a fundamental issue. In two recent papers the authors developed a new blended response algorithm for predicting the response of a nonlinear chaotic forced-dissipative system to small changes in external forcing. This new algorithm is based on the fluctuation–dissipation theorem and combines the geometrically exact general response formula using integration of a linear tangent model at short response times and the classical quasi-Gaussian response algorithm at longer response times. This algorithm overcomes the inherent numerical instability in the geometric formula arising because of positive Lyapunov exponents at longer times while removing potentially large systematic errors from the classical quasi-Gaussian approximation at moderate times. Here the new blended method is tested on the low-frequency response for a T21 barotropic truncation on the sphere with realistic topography in two dynamical regimes corresponding to the mean climate behavior at 300- and 500-hPa geopotential height. The 300-hPa regime has robust strongly mixing behavior with a nearly Gaussian equilibrium state distribution, whereas the 500-hPa regime is weakly chaotic with slowly decaying time autocorrelation functions and strongly non-Gaussian climatology. It is found that the blended response algorithm has significant skill beyond the classical quasi-Gaussian algorithm for the response of the climate mean state and its variance. Additionally, the predicted response of the T21 barotropic model in the low-frequency regime for these functionals does not seem to be affected by the model’s structural instability. Thus, the results here suggest the use of the fluctuation–dissipation theorem–based blended response algorithm for more complex nonlinear geophysical models.