Two Markov models with different dynamics and forcing are used to model the transient eddy statistics of an idealized general circulation model (GCM). The first Markov model employs a physically based dynamical operator composed of the linearized primitive equations plus spatially uniform damping. This model, when driven by spatially uncorrelated forcing, failed to produce reasonable fluxes and variances, despite tuning of the damping and forcing coefficients. This result contrasts with previous studies that have used the linearized quasigeostrophic equations to model extratropical eddy statistics. The second Markov model is constructed empirically from the time-lagged covariances of the GCM time series. This empirical Markov model could reproduce the dominant covariances over a range of time lags, provided it contained a sufficiently large number of degrees of freedom. it could not, however reproduce the time-lag evolution of the trailing EOFs contained in the model. The errors in the trailing EOFs displayed a systematic behavior that could be explained by assuming that the "effective noise" -the noise required to reproduce the full covariances-is correlated over timescales comparable to the smallest e-folding time of the eigenmodes. Under this assumption, the effective noise is not white, but, for sufficiently large model dimension, the dominant disturbances still can be modeled appropriately by a Markov model because their associated decorrelation;rates are small compared to the decorrelation rate of noise. This explanation is illustrated using a three-variable Markov model. These results suggest the following criteria for Markov model estimation: the lag and number of EOFs should be chosen such that the least damped modes show little or no dependence on lag and that none of the imaginary eigenvalues are aliased (in a sense defined in the paper). The resulting Markov model for the dominant disturbances is not sensitive to EOF truncation or choice of time lag, except for the structure of the singular vectors and adjoints, and the ordering of the eigenmodes. The sensitivity in singular vectors and adjoints is a plausible consequence of nonnormality, as nonnormality of the underlying physical system leads to singular vectors differing considerably from the normal modes and EOFs. The stable eigenmodes resemble the leading EOFs used to construct the empirical model, but differ considerably from the unstable eigenmodes of the linearized GCM. This difference is attributed to nonlinear processes implicitly represented in the Markov model. The dissipation and stochastic forcing were concentrated in the Tropics and subtropics, in contrast to the eddy variance and fluxes, which were concentrated in subtropics and midlatitudes. The associated singular vectors also were localized initially in the Tropics and subtropics, but eventually develop into robust extratropical disturbances. Interestingly, the dominant singular vectors undergo a growth and decay life cycle characteristic of the classic nonlinear life cycle, with time-averaged fluxes in close agreement with those diagnosed from the GCM climatology The fact that the forcing, dissipation, and initial singular vectors are concentrated in the same vicinity suggests a dynamical feedback between Tropics and subtropics.
