Singular Modes and Low-Frequency Atmospheric Variability

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  • 1 Meteorologisches Institut der Universität München, Munich, Germany
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Abstract

Recently, it has been shown that the EOFs (empirical orthogonal functions) of the solutions of a stationary linear model to an ensemble of white noise forcing fields are the Schmidt modes (singular modes) of the model' linear operator. If the forcing is not pure white noise, this exact association breaks down. In this paper, the role of these singular modes for the recurring modes of the solutions in the latter case is investigated.

First, a steady-state barotropic model, linearized about a wavy 300-mb basic state, is forced by a large sample of quasi-stationary vorticity forcings where the basic state and the forcing are both derived from a climate control run of the Hamburg ECHAM2 GCM. The EOFs of this sample of solutions are explicitly calculated and the leading EOF obtained turns out to be very similar to the leading singular mode of the model. The primary energy source of this mode is the conversion of the kinetic energy of the zonally asymmetric components of the basic state to the mode. On the other hand, the second EOF matches closely to the leading mode of the GCM's low-frequency variability. This second EOF occurs primarily due to the action of the forcing.

Then, the sensitivity of the singular modes to variations of the dissipation parameters and the basic state is investigated. Thereby, it is found that it is essential to retain the zonally inhomogeneous components of the basic state. With the wavy basic state, it is found that for sufficiently strong dissipation the leading singular mode becomes very similar to the leading mode of the GCM's low-frequency variability if an equivalent-barotropic basic state is used. Such a similarity cannot be achieved for a 300-mb basic state. Moreover, it also turns out that the quasi-stationary forcing associated with the GCM variability mode is able to excite the leading singular mode of the linear model.

It is suggested that the linear singular modes, via the conversion of kinetic energy of the wavy basic state, provide some of the fundamental structures into which observed low-frequency modes are organized in the real (nonlinear) world, too.

Abstract

Recently, it has been shown that the EOFs (empirical orthogonal functions) of the solutions of a stationary linear model to an ensemble of white noise forcing fields are the Schmidt modes (singular modes) of the model' linear operator. If the forcing is not pure white noise, this exact association breaks down. In this paper, the role of these singular modes for the recurring modes of the solutions in the latter case is investigated.

First, a steady-state barotropic model, linearized about a wavy 300-mb basic state, is forced by a large sample of quasi-stationary vorticity forcings where the basic state and the forcing are both derived from a climate control run of the Hamburg ECHAM2 GCM. The EOFs of this sample of solutions are explicitly calculated and the leading EOF obtained turns out to be very similar to the leading singular mode of the model. The primary energy source of this mode is the conversion of the kinetic energy of the zonally asymmetric components of the basic state to the mode. On the other hand, the second EOF matches closely to the leading mode of the GCM's low-frequency variability. This second EOF occurs primarily due to the action of the forcing.

Then, the sensitivity of the singular modes to variations of the dissipation parameters and the basic state is investigated. Thereby, it is found that it is essential to retain the zonally inhomogeneous components of the basic state. With the wavy basic state, it is found that for sufficiently strong dissipation the leading singular mode becomes very similar to the leading mode of the GCM's low-frequency variability if an equivalent-barotropic basic state is used. Such a similarity cannot be achieved for a 300-mb basic state. Moreover, it also turns out that the quasi-stationary forcing associated with the GCM variability mode is able to excite the leading singular mode of the linear model.

It is suggested that the linear singular modes, via the conversion of kinetic energy of the wavy basic state, provide some of the fundamental structures into which observed low-frequency modes are organized in the real (nonlinear) world, too.

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