Newman, M., P. D. Sardeshmukh, and C. Penland, 1997: Stochastic forcing of the wintertime extratropical flow. J. Atmos. Sci., 54, 435-455.
This study is concerned with assessing the extent to which extratropical low-frequency variability may be viewed as a response to geographically coherent stochastic forcing. This issue is examined with a barotropic model linearized about the long-term mean wintertime 300-mb flow with zonal and meridional structure. The perturbation eigenfunctions of the model are stable (i.e., decaying) for a realistic 5-day drag, so transient eddy activity can be maintained against the drag only with forcing. In a statistical steady state, a fluctuation-dissipation relation (FDR) links the covariance structure of the eddy vorticity to the covariance structure of the forcing. This relation is used in a forward sense to determine the covariance of eddy vorticity for a specified covariance of forcing. It is also used in a backward sense to infer the covariance of forcing required to maintain the observed covariance of eddy vorticity. The focus is on explaining the observed variability of 10-day running mean anomalies of the 300-mb flow in the northern winters of 1985-93.
When used in the backward sense described above, the FDR yields a forcing covariance matrix that is not quite positive definite. This immediately implies that the low-frequency variability cannot be rigorously viewed as a linear barotropic response to white noise forcing. Nonetheless, retaining only the positive definite part of the forcing matrix and using the forward FDR gives a reasonable approximation to the observed vorticity covariance. The approximation can be improved by specifying a stronger drag in the barotropic model. However, the simulation of the 5-day lag covariance of vorticity, which is poor using the 5-day drag, is made worse with the stronger drag. In other words this model cannot correctly simulate the time development of low-frequency variability. Thus extratropical low-frequency variability cannot be understood as a linear barotropic response to geographically coherent white noise forcing.
A slightly red stochastic forcing, with a decorrelation timescale of 1-2 days, produces only a modest improvement in the 5-day lag results. A very red forcing, with a decorrelation timescale of 20 days, gives better results at 0- and 5-day lags, but not at 10- or 20-day lags. Modeling the forcing separately as a first-order Markov process, with the model parameters estimated from observations, gives almost perfect results at 0- and 5-day lags. However, further analysis shows this to be an artifact of comparing the empirical-dynamical model simulations with dependent data. When the noise model parameters estimated from one-half of the data record are used to explain low-frequency variability in the other, the results are again poor. It is concluded that extratropical low-frequency variability cannot be viewed as randomly forced barotropic Rossby waves evolving on a zonally and meridionally varying climatological 300-mb flow. The spatial and temporal structure of the observed variability cannot be explained without also taking into account the detailed spatial and temporal structure of the forcing, respectively.